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MySQL 9.1 Reference Manual

15.8.2 EXPLAIN Statement

{EXPLAIN | DESCRIBE | DESC}tbl_name [col_name |wild]{EXPLAIN | DESCRIBE | DESC}    [explain_type] [INTOvariable]    {[schema_spec]explainable_stmt | FOR CONNECTIONconnection_id}{EXPLAIN | DESCRIBE | DESC} ANALYZE [FORMAT = TREE] [schema_spec]select_statement{EXPLAIN | DESCRIBE | DESC} ANALYZE FORMAT = JSON INTOvariable [schema_spec]select_statementexplain_type: {    FORMAT =format_name}format_name: {    TRADITIONAL  | JSON  | TREE}explainable_stmt: {    SELECT statement  | TABLE statement  | DELETE statement  | INSERT statement  | REPLACE statement  | UPDATE statement}schema_spec:FOR {SCHEMA | DATABASE}schema_name

TheDESCRIBE andEXPLAIN statements are synonyms. In practice, theDESCRIBE keyword is more often used to obtain information about table structure, whereasEXPLAIN is used to obtain a query execution plan (that is, an explanation of how MySQL would execute a query).

The following discussion uses theDESCRIBE andEXPLAIN keywords in accordance with those uses, but the MySQL parser treats them as completely synonymous.

Obtaining Table Structure Information

DESCRIBE provides information about the columns in a table:

mysql> DESCRIBE City;+------------+----------+------+-----+---------+----------------+| Field      | Type     | Null | Key | Default | Extra          |+------------+----------+------+-----+---------+----------------+| Id         | int(11)  | NO   | PRI | NULL    | auto_increment || Name       | char(35) | NO   |     |         |                || Country    | char(3)  | NO   | UNI |         |                || District   | char(20) | YES  | MUL |         |                || Population | int(11)  | NO   |     | 0       |                |+------------+----------+------+-----+---------+----------------+

DESCRIBE is a shortcut forSHOW COLUMNS. These statements also display information for views. The description forSHOW COLUMNS provides more information about the output columns. SeeSection 15.7.7.6, “SHOW COLUMNS Statement”.

By default,DESCRIBE displays information about all columns in the table.col_name, if given, is the name of a column in the table. In this case, the statement displays information only for the named column.wild, if given, is a pattern string. It can contain the SQL% and_ wildcard characters. In this case, the statement displays output only for the columns with names matching the string. There is no need to enclose the string within quotation marks unless it contains spaces or other special characters.

TheDESCRIBE statement is provided for compatibility with Oracle.

TheSHOW CREATE TABLE,SHOW TABLE STATUS, andSHOW INDEX statements also provide information about tables. SeeSection 15.7.7, “SHOW Statements”.

Theexplain_format system variable has no effect on the output ofEXPLAIN when used to obtain information about table columns.

Obtaining Execution Plan Information

TheEXPLAIN statement provides information about how MySQL executes statements:

EXPLAIN works withSELECT,DELETE,INSERT,REPLACE,UPDATE, andTABLE statements.
WhenEXPLAIN is used with an explainable statement, MySQL displays information from the optimizer about the statement execution plan. That is, MySQL explains how it would process the statement, including information about how tables are joined and in which order. For information about usingEXPLAIN to obtain execution plan information, seeSection 10.8.2, “EXPLAIN Output Format”.
WhenEXPLAIN is used withFOR CONNECTIONconnection_id rather than an explainable statement, it displays the execution plan for the statement executing in the named connection. SeeSection 10.8.4, “Obtaining Execution Plan Information for a Named Connection”.
For explainable statements,EXPLAIN produces additional execution plan information that can be displayed usingSHOW WARNINGS. SeeSection 10.8.3, “Extended EXPLAIN Output Format”.
EXPLAIN is useful for examining queries involving partitioned tables. SeeSection 26.3.5, “Obtaining Information About Partitions”.

TheFORMAT option can be used to select the output format.TRADITIONAL presents the output in tabular format. This is the default if noFORMAT option is present.JSON format displays the information in JSON format.TREE provides tree-like output with more precise descriptions of query handling than theTRADITIONAL format; it is the only format which shows hash join usage (seeSection 10.2.1.4, “Hash Join Optimization”) and is always used forEXPLAIN ANALYZE.

In MySQL 9.1, the default output format used byEXPLAIN (that is, when it has noFORMAT option) is determined by the value of theexplain_format system variable. The precise effects of this variable are described later in this section.

MySQL 9.1 supports an additionalINTO option withEXPLAIN FORMAT=JSON, which enables saving the JSON formatted output into a user variable, like this:

mysql> EXPLAIN FORMAT=JSON INTO @myselect     ->     SELECT name FROM a WHERE id = 2;Query OK, 0 rows affected (0.00 sec)mysql> SELECT @myselect\G*************************** 1. row ***************************@myex: {  "query_block": {    "select_id": 1,    "cost_info": {      "query_cost": "1.00"    },    "table": {      "table_name": "a",      "access_type": "const",      "possible_keys": [        "PRIMARY"      ],      "key": "PRIMARY",      "used_key_parts": [        "id"      ],      "key_length": "4",      "ref": [        "const"      ],      "rows_examined_per_scan": 1,      "rows_produced_per_join": 1,      "filtered": "100.00",      "cost_info": {        "read_cost": "0.00",        "eval_cost": "0.10",        "prefix_cost": "0.00",        "data_read_per_join": "408"      },      "used_columns": [        "id",        "name"      ]    }  }}1 row in set (0.00 sec)

This works with any explainable statement (SELECT,TABLE,INSERT,UPDATE,REPLACE, orDELETE). Examples usingUPDATE andDELETE statements are shown here:

mysql> EXPLAIN FORMAT=JSON INTO @myupdate     ->   UPDATE a SET name2 = "garcia" WHERE id = 3;              Query OK, 0 rows affected (0.00 sec)mysql> EXPLAIN FORMAT=JSON INTO @mydelete     ->     DELETE FROM a WHERE name1 LIKE '%e%';Query OK, 0 rows affected (0.00 sec)mysql> SELECT @myupdate, @mydelete\G*************************** 1. row ***************************@myupdate: {  "query_block": {    "select_id": 1,    "table": {      "update": true,      "table_name": "a",      "access_type": "range",      "possible_keys": [        "PRIMARY"      ],      "key": "PRIMARY",      "used_key_parts": [        "id"      ],      "key_length": "4",      "ref": [        "const"      ],      "rows_examined_per_scan": 1,      "filtered": "100.00",      "attached_condition": "(`db`.`a`.`id` = 3)"    }  }}@mydelete: {  "query_block": {    "select_id": 1,    "table": {      "delete": true,      "table_name": "a",      "access_type": "ALL",      "rows_examined_per_scan": 2,      "filtered": "100.00",      "attached_condition": "(`db`.`a`.`name1` like '%e%')"    }  }}1 row in set (0.00 sec)

You can work with this value using MySQL JSON functions as you would with any other JSON value, as in these examples usingJSON_EXTRACT():

mysql> SELECT JSON_EXTRACT(@myselect, "$.query_block.table.key");+----------------------------------------------------+| JSON_EXTRACT(@myselect, "$.query_block.table.key") |+----------------------------------------------------+| "PRIMARY"                                          |+----------------------------------------------------+1 row in set (0.01 sec)mysql> SELECT JSON_EXTRACT(@myupdate, "$.query_block.table.access_type") AS U_acc,    ->        JSON_EXTRACT(@mydelete, "$.query_block.table.access_type") AS D_acc;+---------+-------+| U_acc   | D_acc |+---------+-------+| "range" | "ALL" |+---------+-------+1 row in set (0.00 sec)

For complex statements, the JSON output can be quite large; in particular, it can be difficult when reading it to pair the closing bracket and opening brackets; to cause the JSON structure's key, if it has one, to be repeated near the closing bracket, setend_markers_in_json=ON. You should be aware that while this makes the output easier to read, it also renders the JSON invalid, causing JSON functions to raise an error.

Trying to use anINTO clause without explicitly includingFORMAT=JSON causesEXPLAIN to be rejected withER_EXPLAIN_INTO_IMPLICIT_FORMAT_NOT_SUPPORTED. This is true regardless of the current value of theexplain_format system variable.

TheINTO clause is not supported withFOR CONNECTION.

INTO is also not supported withEXPLAIN ANALYZE whenexplain_json_format_version=1.

Important

If, for any reason, the statement to be analyzed is rejected, the user variable is not updated.

MySQL 9.1 supports aFOR SCHEMA clause, which causesEXPLAIN to behave as if the statement to be analyzed had been executed in the named database;FOR DATABASE is supported as a synonym. A simple example of use is shown here:

mysql> USE b;Database changedmysql> CREATE SCHEMA s1;Query OK, 1 row affected (0.01 sec)mysql> CREATE SCHEMA s2;Query OK, 1 row affected (0.01 sec)mysql> USE s1;Database changedmysql> CREATE TABLE t (c1 INT NOT NULL AUTO_INCREMENT PRIMARY KEY, c2 INT NOT NULL);Query OK, 0 rows affected (0.04 sec)mysql> USE s2;Database changedmysql> CREATE TABLE t (c1 INT NOT NULL AUTO_INCREMENT PRIMARY KEY, c2 INT NOT NULL, KEY i1 (c2));Query OK, 0 rows affected (0.04 sec)mysql> USE b;Database changedmysql> EXPLAIN FORMAT=TREE FOR SCHEMA s1 SELECT * FROM t WHERE c2 > 50\G*************************** 1. row ***************************EXPLAIN: -> Filter: (t.c2 > 50)  (cost=0.35 rows=1)    -> Table scan on t  (cost=0.35 rows=1)1 row in set (0.00 sec)mysql> EXPLAIN FORMAT=TREE FOR SCHEMA s2 SELECT * FROM t WHERE c2 > 50\G*************************** 1. row ***************************EXPLAIN: -> Filter: (t.c2 > 50)  (cost=0.35 rows=1)    -> Covering index scan on t using i1  (cost=0.35 rows=1)1 row in set (0.00 sec)

If the database does not exist, the statement is rejected withER_BAD_DB_ERROR. If the user does not have the necessary privileges to run the statement, it is rejected withER_DBACCESS_DENIED_ERROR.

FOR SCHEMA is not compatible withFOR CONNECTION.

EXPLAIN requires the same privileges required to execute the explained statement. Additionally,EXPLAIN also requires theSHOW VIEW privilege for any explained view.EXPLAIN ... FOR CONNECTION also requires thePROCESS privilege if the specified connection belongs to a different user.

Theexplain_format system variable determines the format of the output fromEXPLAIN when used to display a query execution plan. This variable can take any of the values used with theFORMAT option, with the addition ofDEFAULT as a synonym forTRADITIONAL. The following example uses thecountry table from theworld database which can be obtained fromMySQL: Other Downloads:

mysql> USE world; # Make world the current databaseDatabase changed

Checking the value ofexplain_format, we see that it has the default value, and thatEXPLAIN (with noFORMAT option) therefore uses the traditional tabular output:

mysql> SELECT @@explain_format;+------------------+| @@explain_format |+------------------+| TRADITIONAL      |+------------------+1 row in set (0.00 sec)mysql> EXPLAIN SELECT Name FROM country WHERE Code Like 'A%';+----+-------------+---------+------------+-------+---------------+---------+---------+------+------+----------+-------------+| id | select_type | table   | partitions | type  | possible_keys | key     | key_len | ref  | rows | filtered | Extra       |+----+-------------+---------+------------+-------+---------------+---------+---------+------+------+----------+-------------+|  1 | SIMPLE      | country | NULL       | range | PRIMARY       | PRIMARY | 12      | NULL |   17 |   100.00 | Using where |+----+-------------+---------+------------+-------+---------------+---------+---------+------+------+----------+-------------+1 row in set, 1 warning (0.00 sec)

If we set the value ofexplain_format toTREE, then rerun the sameEXPLAIN statement, the output uses the tree-like format:

mysql> SET @@explain_format=TREE;Query OK, 0 rows affected (0.00 sec)mysql> SELECT @@explain_format;+------------------+| @@explain_format |+------------------+| TREE             |+------------------+1 row in set (0.00 sec)mysql> EXPLAIN SELECT Name FROM country WHERE Code LIKE 'A%';+--------------------------------------------------------------------------------------------------------------+| EXPLAIN                                                                                                      |+--------------------------------------------------------------------------------------------------------------+| -> Filter: (country.`Code` like 'A%')  (cost=3.67 rows=17)    -> Index range scan on country using PRIMARY over ('A' <= Code <= 'A????????')  (cost=3.67 rows=17)  |+--------------------------------------------------------------------------------------------------------------+1 row in set, 1 warning (0.00 sec)

As stated previously, theFORMAT option overrides this setting. Executing the sameEXPLAIN statement usingFORMAT=JSON instead ofFORMAT=TREE shows that this is the case:

mysql> EXPLAIN FORMAT=JSON SELECT Name FROM country WHERE Code LIKE 'A%';+------------------------------------------------------------------------------+| EXPLAIN                                                                      |+------------------------------------------------------------------------------+| {  "query_block": {    "select_id": 1,    "cost_info": {      "query_cost": "3.67"    },    "table": {      "table_name": "country",      "access_type": "range",      "possible_keys": [        "PRIMARY"      ],      "key": "PRIMARY",      "used_key_parts": [        "Code"      ],      "key_length": "12",      "rows_examined_per_scan": 17,      "rows_produced_per_join": 17,      "filtered": "100.00",      "cost_info": {        "read_cost": "1.97",        "eval_cost": "1.70",        "prefix_cost": "3.67",        "data_read_per_join": "16K"      },      "used_columns": [        "Code",        "Name"      ],      "attached_condition": "(`world`.`country`.`Code` like 'A%')"    }  }}                                                                              |+------------------------------------------------------------------------------+1 row in set, 1 warning (0.00 sec)

To return the default output ofEXPLAIN to the tabular format, setexplain_format toTRADITIONAL. Alternatively, you can set it toDEFAULT, which has the same effect, as shown here:

mysql> SET @@explain_format=DEFAULT;Query OK, 0 rows affected (0.00 sec)mysql> SELECT @@explain_format;+------------------+| @@explain_format |+------------------+| TRADITIONAL      |+------------------+1 row in set (0.00 sec)

MySQL 9.1 supports two versions of the JSON output format. Version 1 is the linear format always used in MySQL 8.2 and earlier; this remains the default in MySQL 9.1, and is used in the examples already shown in this section. Version 2 of the JSON output format is based on access paths, and is intended to provide compatibility with future versions of the MySQL Optimizer. You can switch to the Version 2 format by setting the value of theexplain_json_format_version server system variable to2, as shown here for the sameEXPLAIN statement used in the previous example:

mysql> SELECT @@explain_json_format_version;+-------------------------------+| @@explain_json_format_version |+-------------------------------+|                             1 |+-------------------------------+1 row in set (0.00 sec)mysql> SET @@explain_json_format_version = 2;Query OK, 0 rows affected (0.00 sec)mysql> SELECT @@explain_json_format_version;+-------------------------------+| @@explain_json_format_version |+-------------------------------+|                             2 |+-------------------------------+1 row in set (0.00 sec)mysql> EXPLAIN FORMAT=JSON SELECT Name FROM country WHERE Code LIKE 'A%';+------------------------------------------------------------------------------+| EXPLAIN                                                                      |+------------------------------------------------------------------------------+| {  "query": "/* select#1 */ select `world`.`country`.`Name` AS `Name` from `world`.`country` where (`world`.`country`.`Code` like 'A%')",  "inputs": [    {      "ranges": [        "('A' <= Code <= 'A????????')"      ],      "covering": false,      "operation": "Index range scan on country using PRIMARY over ('A' <= Code < 'A????????')",      "index_name": "PRIMARY",      "table_name": "country",      "access_type": "index",      "estimated_rows": 17.0,      "index_access_type": "index_range_scan",      "estimated_total_cost": 3.668778400708174    }  ],  "condition": "(country.`Code` like 'A%')",  "operation": "Filter: (country.`Code` like 'A%')",  "access_type": "filter",  "estimated_rows": 17.0,  "estimated_total_cost": 3.668778400708174}                                                                              |+------------------------------------------------------------------------------+

Settingexplain_json_format_version = 2 also enables support for anINTO clause withEXPLAIN ANALYZE FORMAT=JSON, which enables you to store the JSON output in a user variable, as shown here:

mysql> EXPLAIN ANALYZE FORMAT=JSON INTO @v1    ->   SELECT Name FROM country WHERE Code LIKE 'A%'\G*************************** 1. row ***************************@v1: {  "query": "/* select#1 */ select `world`.`country`.`Name` AS `Name` from `world`.`country` where (`world`.`country`.`Code` like 'A%')",  "inputs": [    {      "ranges": [        "('A' <= Code <= 'A????????')"      ],      "covering": false,      "operation": "Index range scan on country using PRIMARY over ('A' <= Code <= 'A????????')",      "index_name": "PRIMARY",      "table_name": "country",      "access_type": "index",      "actual_rows": 17.0,      "key_columns": [        "Code"      ],      "schema_name": "world",      "actual_loops": 1,      "used_columns": [        "Code",        "Name"      ],      "estimated_rows": 17.0,      "index_access_type": "index_range_scan",      "actual_last_row_ms": 0.097402,      "actual_first_row_ms": 0.08752700000000001,      "estimated_total_cost": 3.668778400708174    }  ],  "condition": "(country.`Code` like 'A%')",  "operation": "Filter: (country.`Code` like 'A%')",  "query_type": "select",  "access_type": "filter",  "actual_rows": 17.0,  "actual_loops": 1,  "estimated_rows": 17.0,  "filter_columns": [    "world.country.`Code`"  ],  "actual_last_row_ms": 0.10903299999999999,  "actual_first_row_ms": 0.09328499999999999,  "estimated_total_cost": 3.668778400708174}

You can use the variable as an argument to JSON functions to obtain specific items of information from the value, like this:

mysql> SELECT JSON_EXTRACT(@v1,'$.index_name') AS iname,    ->        JSON_EXTRACT(@v1, '$.table_name') AS tname\G*************************** 1. row ***************************iname: "PRIMARY"tname: "country"1 row in set (0.00 sec)

This form ofEXPLAIN ANALYZE requires an explicitFORMAT=JSON clause, and is supported only withSELECT statements. An optionalFOR SCHEMA option is also supported, but not required. (FOR DATABASE can also be used, instead.) TheINTO clause is supported withFORMAT=JSON only whenexplain_json_format_version is equal to 2; otherwise the statement fails withEXPLAIN ANALYZE does not support FORMAT=JSON with explain_json_format_version=1 (ER_EXPLAIN_ANALYZE_JSON_FORMAT_VERSION_NOT_SUPPORTED).

After using the Version 2 format, you can cause the JSON output from all subsequentEXPLAIN FORMAT=JSON statements to revert to the Version 1 format by settingexplain_json_format_version back to1 (the default).

The value ofexplain_json_format_version determines the version of the JSON output format employed by allEXPLAIN statements which use it, whether the JSON format is used because a givenEXPLAIN statement includes an explicitFORMAT=JSON option, or because the JSON format is used automatically due to theexplain_format system variable being set toJSON.

With the help ofEXPLAIN, you can see where you should add indexes to tables so that the statement executes faster by using indexes to find rows. You can also useEXPLAIN to check whether the optimizer joins the tables in an optimal order. To give a hint to the optimizer to use a join order corresponding to the order in which the tables are named in aSELECT statement, begin the statement withSELECT STRAIGHT_JOIN rather than justSELECT. (SeeSection 15.2.13, “SELECT Statement”.)

The optimizer trace may sometimes provide information complementary to that ofEXPLAIN. However, the optimizer trace format and content are subject to change between versions. For details, seeSection 10.15, “Tracing the Optimizer”.

If you have a problem with indexes not being used when you believe that they should be, runANALYZE TABLE to update table statistics, such as cardinality of keys, that can affect the choices the optimizer makes. SeeSection 15.7.3.1, “ANALYZE TABLE Statement”.

Note

MySQL Workbench has a Visual Explain capability that provides a visual representation ofEXPLAIN output. SeeTutorial: Using Explain to Improve Query Performance.

Obtaining Information with EXPLAIN ANALYZE

EXPLAIN ANALYZE runs a statement and producesEXPLAIN output along with timing and additional, iterator-based, information about how the optimizer's expectations matched the actual execution. For each iterator, the following information is provided:

Estimated execution cost
(Some iterators are not accounted for by the cost model, and so are not included in the estimate.)
Estimated number of returned rows
Time to return first row
Time spent executing this iterator (including child iterators, but not parent iterators), in milliseconds.
(When there are multiple loops, this figure shows the average time per loop.)
Number of rows returned by the iterator
Number of loops

The query execution information is displayed using theTREE output format, in which nodes represent iterators.EXPLAIN ANALYZE uses an output format which can optionally be specified explicitly usingFORMAT=TREE orFORMAT=JSON; the default isTREE.FORMAT=JSON can be used only ifexplain_json_format_version is set to 2.

EXPLAIN ANALYZE can be used withSELECT statements, multi-tableUPDATE andDELETE statements, andTABLE statements.

You can terminate this statement usingKILL QUERY orCTRL-C.

EXPLAIN ANALYZE cannot be used withFOR CONNECTION.

Example output:

mysql> SELECT @@explain_format;+------------------+| @@explain_format |+------------------+| TRADITIONAL      |+------------------+mysql> EXPLAIN ANALYZE SELECT * FROM t1 JOIN t2 ON (t1.c1 = t2.c2)\G*************************** 1. row ***************************EXPLAIN: -> Inner hash join (t2.c2 = t1.c1)  (cost=3.5 rows=5) (actual time=0.121..0.131 rows=1 loops=1)     -> Table scan on t2  (cost=0.07 rows=5) (actual time=0.0126..0.0221 rows=5 loops=1)     -> Hash        -> Table scan on t1  (cost=0.75 rows=5) (actual time=0.0372..0.0534 rows=5 loops=1)mysql> EXPLAIN ANALYZE FORMAT=TREE SELECT * FROM t3 WHERE i > 8\G*************************** 1. row ***************************EXPLAIN: -> Filter: (t3.i > 8)  (cost=0.75 rows=1.67) (actual time=0.0484..0.0542 rows=1 loops=1)    -> Table scan on t3  (cost=0.75 rows=5) (actual time=0.0417..0.0494 rows=5 loops=1)mysql> EXPLAIN ANALYZE FORMAT=JSON SELECT * FROM t3 WHERE pk < 17\G*************************** 1. row ***************************EXPLAIN: {  "query": "/* select#1 */ select `a`.`t3`.`pk` AS `pk`,`a`.`t3`.`i` AS `i` from `a`.`t3` where (`a`.`t3`.`pk` < 17)",  "inputs": [    {      "ranges": [        "(pk < 17)"      ],      "covering": false,      "operation": "Index range scan on t3 using PRIMARY over (pk < 17)",      "index_name": "PRIMARY",      "table_name": "t3",      "access_type": "index",      "actual_rows": 3.0,      "key_columns": [        "pk"      ],      "schema_name": "a",      "actual_loops": 1,      "used_columns": [        "pk",        "i"      ],      "estimated_rows": 3.0,      "index_access_type": "index_range_scan",      "actual_last_row_ms": 0.034214,      "actual_first_row_ms": 0.03052,      "estimated_total_cost": 0.860618301731245    }  ],  "condition": "(t3.pk < 17)",  "operation": "Filter: (t3.pk < 17)",  "query_type": "select",  "access_type": "filter",  "actual_rows": 3.0,  "actual_loops": 1,  "estimated_rows": 3.0,  "filter_columns": [    "a.t3.pk"  ],  "actual_last_row_ms": 0.038189,  "actual_first_row_ms": 0.033429,  "estimated_total_cost": 0.860618301731245}

The tables used in the example output were created by the statements shown here:

CREATE TABLE t1 (    c1 INTEGER DEFAULT NULL,    c2 INTEGER DEFAULT NULL);CREATE TABLE t2 (    c1 INTEGER DEFAULT NULL,    c2 INTEGER DEFAULT NULL);CREATE TABLE t3 (    pk INTEGER NOT NULL PRIMARY KEY,    i INTEGER DEFAULT NULL);

Values shown foractual time in the output of this statement are expressed in milliseconds.

explain_format has the following effects onEXPLAIN ANALYZE:

If the value of this variable isTRADITIONAL orTREE (or the synonymDEFAULT),EXPLAIN ANALYZE uses theTREE format unless the statement includesFORMAT=JSON.
If the value ofexplain_format isJSON,EXPLAIN ANALYZE uses the JSON format unlessFORMAT=TREE is specified as part of the statement.

UsingFORMAT=TRADITIONAL orFORMAT=DEFAULT withEXPLAIN ANALYZE always raises an error, regardless of the value ofexplain_format.

In MySQL 9.1, numbers in the output ofEXPLAIN ANALYZE andEXPLAIN FORMAT=TREE are formatted according to the following rules:

Numbers in the range 0.001-999999.5 are printed as decimal numbers.
Decimal numbers less than 1000 have three significant digits; the remainder have four, five, or six.
Numbers outside the range 0.001-999999.5 are printed in engineering format. Examples of such values are1.23e+9 and934e-6.
No trailing zeros are printed. For example, we print2.3 rather than2.30, and1.2e+6 rather than1.20e+6.
Numbers less than1e-12 are printed as0.

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