Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
62.5%	6.2%	31.3%	6
65.6%	3.1%	31.3%	7
65.6%	1.6%	32.8%	8
66.4%	0.8%	32.8%	9
66.4%	0.4%	33.2%	10
66.6%	0.2%	33.2%	11
66.6%	0.1%	33.3%	12
66.6%	0%	33.3%	13
66.6%	0%	33.3%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample13.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 23 to 18 computations (21.7% saved)

simplify232.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	4718	13
1	4718	13

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 2

Compiler

Compiled 29 to 24 computations (17.2% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 4647935950575487/36028797018963968 (pow.f64 x 3))
0.0b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)))
0.0b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)))
0.1b	(*.f64 4647935950575487/36028797018963968 (pow.f64 x 3))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_93`
12×	`associate-r_binary64_11`
7×	`add-exp-log_binary64_109`
6×	`*-un-lft-identity_binary64_71` `add-cube-cbrt_binary64_106`
4×	`add-cbrt-cube_binary64_107` `unswap-sqr_binary64_39` `add-log-exp_binary64_110` `cube-prod_binary64_99` `unpow-prod-down_binary64_150`
3×	`associate-l_binary64_12` `prod-exp_binary64_120`
2×	`sqr-pow_binary64_43` `pow1_binary64_132`
1×	`pow-exp_binary64_139` `cube-mult_binary64_101` `pow-to-exp_binary64_140` `flip--_binary64_46` `unpow3_binary64_137` `*-commutative_binary64_2` `flip3--_binary64_75` `cbrt-unprod_binary64_104` `cancel-sign-sub-inv_binary64_37` `diff-log_binary64_163` `sub-neg_binary64_64`

Counts

2 → 43

Calls

4 calls:

7.0ms	(*.f64 4647935950575487/36028797018963968 (pow.f64 x 3))
4.0ms	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)))
0.0ms	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)))
0.0ms	(*.f64 4647935950575487/36028797018963968 (pow.f64 x 3))

series108.0ms (3.4%)

Counts

2 → 9

Calls

2 calls:

77.0ms	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)))
31.0ms	(*.f64 4647935950575487/36028797018963968 (pow.f64 x 3))

Compiler

Compiled 121 to 109 computations (9.9% saved)

simplify92.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4867	584
1	4867	584

prune69.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	48	4	52
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	49	5	54

Error

Counts

54 → 5

Compiler

Compiled 724 to 552 computations (23.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4647935950575487/36028797018963968 x) (*.f64 x x))
0.0b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 (.f64 4647935950575487/36028797018963968 x) (.f64 x x)))
0.0b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 (.f64 4647935950575487/36028797018963968 x) (.f64 x x)))
0.2b	(.f64 (.f64 4647935950575487/36028797018963968 x) (*.f64 x x))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_107` `add-exp-log_binary64_109` `pow1_binary64_132`
8×	`prod-exp_binary64_120` `cbrt-unprod_binary64_104` `pow-prod-down_binary64_142`
4×	`add-log-exp_binary64_110`
2×	`*-un-lft-identity_binary64_71` `add-cube-cbrt_binary64_106` `add-sqr-sqrt_binary64_93`
1×	`flip--_binary64_46` `associate-r_binary64_11` `associate-l_binary64_12` `*-commutative_binary64_2` `flip3--_binary64_75` `cancel-sign-sub-inv_binary64_37` `diff-log_binary64_163` `sub-neg_binary64_64`

Counts

2 → 34

Calls

4 calls:

7.0ms	(.f64 (.f64 4647935950575487/36028797018963968 x) (*.f64 x x))
4.0ms	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 (.f64 4647935950575487/36028797018963968 x) (.f64 x x)))
0.0ms	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 (.f64 4647935950575487/36028797018963968 x) (.f64 x x)))
0.0ms	(.f64 (.f64 4647935950575487/36028797018963968 x) (*.f64 x x))

series105.0ms (3.3%)

Counts

2 → 9

Calls

2 calls:

73.0ms	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 (.f64 4647935950575487/36028797018963968 x) (.f64 x x)))
32.0ms	(.f64 (.f64 4647935950575487/36028797018963968 x) (*.f64 x x))

Compiler

Compiled 121 to 109 computations (9.9% saved)

simplify75.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5542	478

prune41.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	44	4	48

Error

Counts

48 → 4

Compiler

Compiled 550 to 399 computations (27.5% saved)

localize7.0ms (0.2%)

Local error

Found 6 expressions with local error:

20.8b	(cbrt.f64 (*.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9)))
0.1b	(*.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9))
0.0b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (cbrt.f64 (.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9))))
0.0b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (cbrt.f64 (.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9))))
0.1b	(*.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9))
20.8b	(cbrt.f64 (*.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9)))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_93`
8×	`add-exp-log_binary64_109`
7×	`associate-r_binary64_11` `*-un-lft-identity_binary64_71` `add-cube-cbrt_binary64_106`
5×	`add-cbrt-cube_binary64_107` `add-log-exp_binary64_110`
4×	`unpow-prod-down_binary64_150` `cancel-sign-sub-inv_binary64_37`
3×	`unswap-sqr_binary64_39` `associate-l_binary64_12` `prod-exp_binary64_120` `pow1_binary64_132`
2×	`cbrt-prod_binary64_102` `sqr-pow_binary64_43`
1×	`pow-exp_binary64_139` `pow-to-exp_binary64_140` `flip--_binary64_46` `pow1/3_binary64_153` `*-commutative_binary64_2` `flip3--_binary64_75` `cbrt-unprod_binary64_104` `diff-log_binary64_163` `sub-neg_binary64_64`

Counts

3 → 49

Calls

6 calls:

6.0ms	(*.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9))
4.0ms	(-.f64 (.f64 2150310427208497/2251799813685248 x) (cbrt.f64 (.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9))))
3.0ms	(cbrt.f64 (*.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9)))
0.0ms	(-.f64 (.f64 2150310427208497/2251799813685248 x) (cbrt.f64 (.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9))))
0.0ms	(*.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9))

series170.0ms (5.3%)

Counts

3 → 12

Calls

3 calls:

82.0ms

(-.f64 (*.f64 2150310427208497/2251799813685248 x) (cbrt.f64 (*.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9))))

44.0ms

(*.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9))

44.0ms

(cbrt.f64 (*.f64 100410794696347307466492240129774699304007026303/46768052394588893382517914646921056628989841375232 (pow.f64 x 9)))

Compiler

Compiled 201 to 183 computations (9% saved)

simplify85.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4897	763
1	4897	763

prune55.0ms (1.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	61	4	65

Error

Counts

65 → 4

Compiler

Compiled 868 to 711 computations (18.1% saved)

localize9.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (*.f64 x x) -4647935950575487/36028797018963968))))
0.1b	(sqrt.f64 (.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (*.f64 x x) -4647935950575487/36028797018963968))))
0.1b	(.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (*.f64 x x) -4647935950575487/36028797018963968)))
0.1b	(.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (*.f64 x x) -4647935950575487/36028797018963968)))
0.1b	(sqrt.f64 (.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (*.f64 x x) -4647935950575487/36028797018963968))))
0.1b	(.f64 (.f64 x x) -4647935950575487/36028797018963968)
0.1b	(.f64 (.f64 x x) -4647935950575487/36028797018963968)
0.3b	(.f64 (sqrt.f64 (.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (.f64 x x) -4647935950575487/36028797018963968)))) (sqrt.f64 (.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (*.f64 x x) -4647935950575487/36028797018963968)))))

rewrite44.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`pow1_binary64_132`
30×	`sqrt-pow1_binary64_89`
27×	`pow-prod-down_binary64_142`
16×	`add-cbrt-cube_binary64_107` `add-exp-log_binary64_109` `associate-*r/_binary64_13`
14×	`sqrt-div_binary64_88` `add-sqr-sqrt_binary64_93`
11×	`pow1/2_binary64_151`
10×	`associate-r_binary64_11` `*-un-lft-identity_binary64_71` `pow-prod-up_binary64_141` `add-cube-cbrt_binary64_106`
7×	`prod-exp_binary64_120` `flip-+_binary64_45` `cbrt-unprod_binary64_104` `flip3-+_binary64_74`
6×	`pow-sqr_binary64_44` `associate-l_binary64_12`
5×	`sqrt-prod_binary64_87`
4×	`add-log-exp_binary64_110` `frac-times_binary64_81` `swap-sqr_binary64_38`
3×	`unswap-sqr_binary64_39` `*-commutative_binary64_2`
2×	`associate-*l/_binary64_14`
1×	`pow2_binary64_152` `rem-square-sqrt_binary64_83` `pow-plus_binary64_134` `sqrt-unprod_binary64_91`

Counts

4 → 108

Calls

8 calls:

13.0ms	(.f64 (sqrt.f64 (.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (.f64 x x) -4647935950575487/36028797018963968)))) (sqrt.f64 (.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (*.f64 x x) -4647935950575487/36028797018963968)))))
8.0ms	(.f64 (.f64 x x) -4647935950575487/36028797018963968)
7.0ms	(.f64 (.f64 x x) -4647935950575487/36028797018963968)
4.0ms	(sqrt.f64 (.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (*.f64 x x) -4647935950575487/36028797018963968))))
0.0ms	(.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (*.f64 x x) -4647935950575487/36028797018963968)))

series121.0ms (3.8%)

Counts

4 → 14

Calls

4 calls:

47.0ms	(.f64 (sqrt.f64 (.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (.f64 x x) -4647935950575487/36028797018963968)))) (sqrt.f64 (.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (*.f64 x x) -4647935950575487/36028797018963968)))))
29.0ms	(.f64 (.f64 x x) -4647935950575487/36028797018963968)
25.0ms	(.f64 (.f64 x x) -4647935950575487/36028797018963968)
20.0ms	(sqrt.f64 (.f64 x (+.f64 2150310427208497/2251799813685248 (.f64 (*.f64 x x) -4647935950575487/36028797018963968))))

Compiler

Compiled 420 to 344 computations (18.1% saved)

simplify75.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4917	1501
1	4917	1501

prune127.0ms (4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	122	4	126

Error

Counts

126 → 4

Compiler

Compiled 2489 to 1640 computations (34.1% saved)

simplify34.0ms (1.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	959	409
1	959	409

regimes37.0ms (1.2%)

Accuracy

Total 0.1b remaining (97.1%)

Threshold costs 0.1b (97.1%)

Compiler

Compiled 278 to 230 computations (17.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	13
1	37	13

end0.0ms (0%)

sample1.6s (50.9%)

Algorithm

1×

intervals

Results

227.0ms

8000×

body

128

valid

Compiler

Compiled 840 to 694 computations (17.4% saved)

Pareto

0.26712691818799267

Details

analyze4.0ms (0.1%)

sample13.0ms (0.4%)

simplify232.0ms (7.3%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

rewrite13.0ms (0.4%)

series108.0ms (3.4%)

simplify92.0ms (2.9%)

prune69.0ms (2.2%)

localize7.0ms (0.2%)

rewrite14.0ms (0.4%)

series105.0ms (3.3%)

simplify75.0ms (2.4%)

prune41.0ms (1.3%)

localize7.0ms (0.2%)

rewrite16.0ms (0.5%)

series170.0ms (5.3%)

simplify85.0ms (2.7%)

prune55.0ms (1.7%)

localize9.0ms (0.3%)

rewrite44.0ms (1.4%)

series121.0ms (3.8%)

simplify75.0ms (2.4%)

prune127.0ms (4%)

simplify34.0ms (1.1%)

regimes37.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.6s (50.9%)

Profiling