Details

analyze1.1s (16.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5083	96
0	3	3
1	3	3

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)

sample62.0ms (0.9%)

Algorithm

1×

intervals

Results

15.0ms	193×	body	128	valid
14.0ms	32×	body	1024	valid
5.0ms	58×	body	128	invalid
4.0ms	20×	body	512	valid
4.0ms	15×	body	512	invalid
3.0ms	10×	body	1024	invalid
2.0ms	11×	body	256	valid
1.0ms	8×	body	256	invalid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify173.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (167.0ms)

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

28.8b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
3.6b	(.f64 (.f64 x (pow.f64 s 2)) x)
8.6b	(*.f64 x (pow.f64 s 2))
19.6b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite42.0ms (0.6%)

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:

11.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
9.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
6.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
6.0ms	(*.f64 x (pow.f64 s 2))

series185.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
62.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
26.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
24.0ms	(*.f64 x (pow.f64 s 2))

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5001	2228

prune140.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	122	9	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	9	132

Error

1.9b

Counts

132 → 9

Compiler

Compiled 2714 to 1243 computations (54.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
0.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
6.3b	(.f64 s (.f64 c x))
6.3b	(.f64 s (.f64 c x))

rewrite24.0ms (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 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)))))
3.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))

series188.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(/.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))
27.0ms	(.f64 s (.f64 c x))
24.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5021	1306

prune118.0ms (1.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	87	9	96
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	91	14	105

Error

1.7b

Counts

105 → 14

Compiler

Compiled 2181 to 941 computations (56.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))
0.4b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
6.3b	(.f64 s (.f64 c x))
6.3b	(.f64 s (.f64 c x))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
20×	`add-exp-log_binary64_457`
18×	`times-frac_binary64_425` `add-cbrt-cube_binary64_455`
15×	`pow1_binary64_480`
6×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360` `associate-/r_binary64_363` `associate-/l_binary64_364`
4×	`add-log-exp_binary64_458`
3×	`div-exp_binary64_470`
2×	`clear-num_binary64_418` `div-inv_binary64_416` `associate-r_binary64_359` `*-commutative_binary64_350` `frac-2neg_binary64_430` `cbrt-undiv_binary64_453`
1×	`1-exp_binary64_463` `inv-pow_binary64_504` `rec-exp_binary64_469` `pow-flip_binary64_493`

Counts

4 → 94

Calls

4 calls:

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))))
3.0ms	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))

series135.0ms (2%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
26.0ms	(.f64 s (.f64 c x))
25.0ms	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))
24.0ms	(.f64 s (.f64 c x))

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5028	1722

prune125.0ms (1.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	106	14	120

Error

1.7b

Counts

120 → 14

Compiler

Compiled 2981 to 1239 computations (58.4% saved)

localize9.0ms (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))))
0.4b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
6.3b	(.f64 s (.f64 c x))
6.3b	(.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:

6.0ms	(/.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))))

series208.0ms (3%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
56.0ms	(/.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))

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4971	4039
1	4971	4039

prune155.0ms (2.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	144	15	159

Error

1.7b

Counts

159 → 15

Compiler

Compiled 3821 to 1429 computations (62.6% saved)

regimes874.0ms (12.6%)

Accuracy

Total 1.2b remaining (50.8%)

Threshold costs 0b (0%)

Compiler

Compiled 9710 to 6745 computations (30.5% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	33
1	18	33

Compiler

Compiled 42 to 28 computations (33.3% saved)

end0.0ms (0%)

sample2.9s (42.5%)

Algorithm

1×

intervals

Results

490.0ms	6126×	body	128	valid
318.0ms	963×	body	1024	valid
156.0ms	1914×	body	128	invalid
144.0ms	612×	body	512	valid
66.0ms	210×	body	1024	invalid
55.0ms	239×	body	512	invalid
47.0ms	298×	body	256	valid
29.0ms	159×	body	256	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 1616 to 1118 computations (30.8% saved)

Details

analyze1.1s (16.6%)

sample62.0ms (0.9%)

simplify173.0ms (2.5%)

prune3.0ms (0%)

localize11.0ms (0.2%)

rewrite42.0ms (0.6%)

series185.0ms (2.7%)

simplify65.0ms (0.9%)

prune140.0ms (2%)

localize10.0ms (0.1%)

rewrite24.0ms (0.4%)

series188.0ms (2.7%)

simplify66.0ms (1%)

prune118.0ms (1.7%)

localize11.0ms (0.2%)

rewrite24.0ms (0.3%)

series135.0ms (2%)

simplify77.0ms (1.1%)

prune125.0ms (1.8%)

localize9.0ms (0.1%)

rewrite35.0ms (0.5%)

series208.0ms (3%)

simplify90.0ms (1.3%)

prune155.0ms (2.2%)

regimes874.0ms (12.6%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.9s (42.5%)

Profiling