Details

analyze962.0ms (14.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample57.0ms (0.8%)

Algorithm

1×

intervals

Results

18.0ms	196×	body	128	valid
9.0ms	26×	body	1024	valid
5.0ms	69×	body	128	invalid
5.0ms	22×	body	512	valid
3.0ms	11×	body	1024	invalid
2.0ms	12×	body	256	valid
2.0ms	7×	body	512	invalid
1.0ms	7×	body	256	invalid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify266.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (171.0ms)

Iter	Nodes	Cost
0	7278	24

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

23.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
4.0b	(.f64 (.f64 x (pow.f64 s 2)) x)
5.2b	(*.f64 x (pow.f64 s 2))
18.2b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`add-exp-log_binary64_457`
82×	`prod-exp_binary64_468`
34×	`add-cbrt-cube_binary64_455`
18×	`add-sqr-sqrt_binary64_441` `pow-exp_binary64_487` `pow-to-exp_binary64_488`
16×	`cbrt-unprod_binary64_452` `div-exp_binary64_470`
12×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r_binary64_359` `associate-l*_binary64_360`
7×	`unpow-prod-down_binary64_498`
6×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `cbrt-undiv_binary64_453`
3×	`times-frac_binary64_425` `sqr-pow_binary64_391` `-commutative_binary64_350` `unpow2_binary64_484` `associate-/l_binary64_364`
1×	`cos-2_binary64_561` `pow-prod-down_binary64_490` `clear-num_binary64_418` `div-inv_binary64_416` `frac-2neg_binary64_430` `associate-/r*_binary64_363` `div-sub_binary64_424`

Counts

4 → 119

Calls

4 calls:

13.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
11.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
6.0ms	(*.f64 x (pow.f64 s 2))
6.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)

series188.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
63.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
25.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
24.0ms	(*.f64 x (pow.f64 s 2))

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5001	2228

prune135.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	10	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	10	132

Error

2.3b

Counts

132 → 10

Compiler

Compiled 2727 to 1253 computations (54.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
0.3b	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
4.0b	(.f64 s (.f64 c x))
4.0b	(.f64 s (.f64 c x))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
14×	`add-sqr-sqrt_binary64_441`
12×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
9×	`associate-l_binary64_360`
8×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
7×	`pow-prod-down_binary64_490`
5×	`associate-r_binary64_359`
4×	`add-log-exp_binary64_458`
3×	`times-frac_binary64_425` `-commutative_binary64_350` `swap-sqr_binary64_386` `associate-/l_binary64_364`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`cos-2_binary64_561` `clear-num_binary64_418` `div-inv_binary64_416` `unswap-sqr_binary64_387` `sqr-abs_binary64_434` `pow-plus_binary64_482` `frac-2neg_binary64_430` `pow-sqr_binary64_392` `associate-/r*_binary64_363` `pow-prod-up_binary64_489` `pow2_binary64_500` `div-sub_binary64_424`

Counts

4 → 84

Calls

4 calls:

5.0ms	(.f64 s (.f64 c x))
5.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
5.0ms	(.f64 s (.f64 c x))
4.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))

series187.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
27.0ms	(.f64 s (.f64 c x))
25.0ms	(.f64 s (.f64 c x))
24.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5021	1306

prune118.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	86	10	96
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	91	15	106

Error

2.2b

Counts

106 → 15

Compiler

Compiled 2223 to 964 computations (56.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
0.7b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
4.0b	(.f64 s (.f64 c x))
4.0b	(.f64 s (.f64 c x))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64_425`
56×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
21×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
16×	`associate-/l*_binary64_364`
14×	`pow1_binary64_480`
6×	`pow-prod-down_binary64_490` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360` `associate-/r*_binary64_363`
4×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`clear-num_binary64_418` `associate-r_binary64_359` `*-commutative_binary64_350` `frac-2neg_binary64_430`
1×	`associate-/l/_binary64_366`

Counts

4 → 133

Calls

4 calls:

8.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
4.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))

series231.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
64.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
26.0ms	(.f64 s (.f64 c x))
24.0ms	(.f64 s (.f64 c x))

simplify88.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4971	4039
1	4971	4039

prune179.0ms (2.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	140	5	145
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	146	14	160

Error

2.1b

Counts

160 → 14

Compiler

Compiled 4190 to 1659 computations (60.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (fabs.f64 (.f64 s (.f64 c x))) 3/2)
4.0b	(.f64 s (.f64 c x))
4.0b	(.f64 s (.f64 c x))
13.2b	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary64_480`
15×	`add-exp-log_binary64_457`
14×	`add-cbrt-cube_binary64_455`
10×	`add-sqr-sqrt_binary64_441`
9×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360`
4×	`add-log-exp_binary64_458`
3×	`unpow-prod-down_binary64_498` `pow-unpow_binary64_496` `sqrt-prod_binary64_435`
2×	`associate-r_binary64_359` `*-commutative_binary64_350`
1×	`pow1/2_binary64_499` `pow-exp_binary64_487` `sqr-pow_binary64_391` `pow-to-exp_binary64_488` `pow-pow_binary64_491` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 66

Calls

4 calls:

5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
2.0ms	(pow.f64 (fabs.f64 (.f64 s (.f64 c x))) 3/2)
1.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

series127.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow.f64 (fabs.f64 (.f64 s (.f64 c x))) 3/2)
25.0ms	(.f64 s (.f64 c x))
24.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))
24.0ms	(.f64 s (.f64 c x))

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4985	846
1	4985	846

prune81.0ms (1.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	78	14	92

Error

2.1b

Counts

92 → 14

Compiler

Compiled 1898 to 720 computations (62.1% saved)

regimes876.0ms (12.9%)

Accuracy

Total 1.2b remaining (47.9%)

Threshold costs 0b (0%)

Compiler

Compiled 9893 to 6661 computations (32.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	33
1	18	33

end0.0ms (0%)

sample2.9s (43%)

Algorithm

1×

intervals

Results

486.0ms	6112×	body	128	valid
329.0ms	961×	body	1024	valid
158.0ms	1852×	body	128	invalid
150.0ms	604×	body	512	valid
74.0ms	219×	body	1024	invalid
53.0ms	323×	body	256	valid
50.0ms	215×	body	512	invalid
27.0ms	171×	body	256	invalid

Compiler

Compiled 1652 to 1109 computations (32.9% saved)

Details

analyze962.0ms (14.2%)

sample57.0ms (0.8%)

simplify266.0ms (3.9%)

prune3.0ms (0%)

localize12.0ms (0.2%)

rewrite47.0ms (0.7%)

series188.0ms (2.8%)

simplify61.0ms (0.9%)

prune135.0ms (2%)

localize11.0ms (0.2%)

rewrite25.0ms (0.4%)

series187.0ms (2.8%)

simplify64.0ms (0.9%)

prune118.0ms (1.7%)

localize10.0ms (0.1%)

rewrite35.0ms (0.5%)

series231.0ms (3.4%)

simplify88.0ms (1.3%)

prune179.0ms (2.6%)

localize17.0ms (0.3%)

rewrite18.0ms (0.3%)

series127.0ms (1.9%)

simplify72.0ms (1.1%)

prune81.0ms (1.2%)

regimes876.0ms (12.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.9s (43%)

Profiling