Details

analyze936.0ms (13.6%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
37.4%	62.4%	0.1%	10
43.7%	56.2%	0.1%	11
43.7%	56.2%	0.1%	12
43.7%	56.2%	0.1%	13
61.7%	38.2%	0.1%	14

Compiler

Compiled 38 to 30 computations (21.1% saved)

sample30.0ms (0.4%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify137.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5236	55

prune4.0ms (0.1%)

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

30.7b

Counts

2 → 1

Compiler

Compiled 74 to 58 computations (21.6% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
0.1b	(.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)
0.1b	(.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
29.7b	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))

rewrite77.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_12717`
15×	`add-exp-log_binary64_12733` `add-cbrt-cube_binary64_12731`
12×	`*-un-lft-identity_binary64_12695` `add-cube-cbrt_binary64_12730`
10×	`pow1_binary64_12756`
9×	`associate-l_binary64_12636` `associate-r_binary64_12635`
8×	`associate-/l/_binary64_12642` `associate-*l/_binary64_12638`
7×	`flip-+_binary64_12669` `flip3-+_binary64_12698`
4×	`prod-exp_binary64_12744` `frac-times_binary64_12705` `cbrt-unprod_binary64_12728` `add-log-exp_binary64_12734`
3×	`flip3--_binary64_12699` `pow-prod-down_binary64_12766` `-commutative_binary64_12626` `flip--_binary64_12670` `unswap-sqr_binary64_12663` `associate-/r_binary64_12639` `times-frac_binary64_12701`
2×	`div-exp_binary64_12746` `cbrt-undiv_binary64_12729` `associate-/r/_binary64_12641` `associate-*r/_binary64_12637`
1×	`associate-/l*_binary64_12640` `frac-2neg_binary64_12706` `div-inv_binary64_12692` `clear-num_binary64_12694`

Counts

4 → 91

Calls

4 calls:

38.0ms	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))
11.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
10.0ms	(.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)
8.0ms	(.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)

series214.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))
35.0ms	(.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
15.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
14.0ms	(.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)

simplify88.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5260	3047

prune262.0ms (3.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	7	104

Error

0.0b

Counts

104 → 7

Compiler

Compiled 5174 to 3700 computations (28.5% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
0.1b	(.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
0.1b	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
27.5b	(/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))

rewrite71.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_12717`
18×	`*-un-lft-identity_binary64_12695` `add-cube-cbrt_binary64_12730`
12×	`add-exp-log_binary64_12733` `add-cbrt-cube_binary64_12731`
10×	`pow1_binary64_12756`
9×	`associate-l_binary64_12636` `associate-r_binary64_12635` `times-frac_binary64_12701`
6×	`associate-*r/_binary64_12637`
5×	`flip-+_binary64_12669` `flip3-+_binary64_12698`
4×	`add-log-exp_binary64_12734`
3×	`prod-exp_binary64_12744` `associate-/l_binary64_12640` `pow-prod-down_binary64_12766` `-commutative_binary64_12626` `distribute-rgt-in_binary64_12645` `unswap-sqr_binary64_12663` `associate-/r*_binary64_12639` `cbrt-unprod_binary64_12728` `distribute-lft-in_binary64_12644`
2×	`associate-/r/_binary64_12641` `associate-/l/_binary64_12642`
1×	`div-exp_binary64_12746` `cbrt-undiv_binary64_12729` `frac-2neg_binary64_12706` `div-inv_binary64_12692` `clear-num_binary64_12694`

Counts

4 → 97

Calls

4 calls:

31.0ms	(/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
11.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
10.0ms	(.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
7.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))

series199.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
37.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
16.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
14.0ms	(.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4920	3372
1	4920	3372

prune265.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	109	7	116

Error

0.0b

Counts

116 → 7

Compiler

Compiled 5496 to 3943 computations (28.3% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
0.1b	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
0.2b	(.f64 x (.f64 x (+.f64 x 6099563062176297/140737488355328)))
27.5b	(/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (+.f64 (.f64 x (+.f64 (+.f64 (.f64 x (.f64 x (+.f64 x 6099563062176297/140737488355328))) (.f64 x 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))

rewrite69.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_12717`
17×	`*-un-lft-identity_binary64_12695` `add-cube-cbrt_binary64_12730`
15×	`add-exp-log_binary64_12733` `add-cbrt-cube_binary64_12731`
13×	`pow1_binary64_12756`
9×	`associate-l_binary64_12636` `times-frac_binary64_12701`
8×	`associate-*r/_binary64_12637`
7×	`associate-r_binary64_12635`
6×	`distribute-rgt-in_binary64_12645` `distribute-lft-in_binary64_12644`
5×	`prod-exp_binary64_12744` `flip-+_binary64_12669` `pow-prod-down_binary64_12766` `flip3-+_binary64_12698` `cbrt-unprod_binary64_12728`
4×	`add-log-exp_binary64_12734`
3×	`associate-/l_binary64_12640` `-commutative_binary64_12626` `associate-/r*_binary64_12639`
2×	`associate-/r/_binary64_12641` `associate-/l/_binary64_12642` `unswap-sqr_binary64_12663`
1×	`div-exp_binary64_12746` `cbrt-undiv_binary64_12729` `frac-2neg_binary64_12706` `div-inv_binary64_12692` `clear-num_binary64_12694`

Counts

4 → 99

Calls

4 calls:

31.0ms	(/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (+.f64 (.f64 x (+.f64 (+.f64 (.f64 x (.f64 x (+.f64 x 6099563062176297/140737488355328))) (.f64 x 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
11.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
8.0ms	(.f64 x (.f64 x (+.f64 x 6099563062176297/140737488355328)))
7.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))

series209.0ms (3%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (+.f64 (.f64 x (+.f64 (+.f64 (.f64 x (.f64 x (+.f64 x 6099563062176297/140737488355328))) (.f64 x 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
35.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
31.0ms	(.f64 x (.f64 x (+.f64 x 6099563062176297/140737488355328)))
15.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))

simplify100.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5247	3283

prune260.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	111	7	118

Error

0.0b

Counts

118 → 7

Compiler

Compiled 5644 to 4009 computations (29% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
0.1b	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
0.1b	(/.f64 1 (/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328) (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z)))
27.5b	(/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328) (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z))

rewrite98.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64_12701`
64×	`add-sqr-sqrt_binary64_12717`
60×	`*-un-lft-identity_binary64_12695` `add-cube-cbrt_binary64_12730`
21×	`add-exp-log_binary64_12733`
18×	`associate-/r*_binary64_12639`
15×	`add-cbrt-cube_binary64_12731`
11×	`associate-/r/_binary64_12641`
9×	`pow1_binary64_12756`
8×	`div-exp_binary64_12746` `flip-+_binary64_12669` `flip3-+_binary64_12698`
6×	`associate-l_binary64_12636` `associate-/l_binary64_12640` `div-inv_binary64_12692` `associate-r*_binary64_12635`
4×	`cbrt-undiv_binary64_12729` `add-log-exp_binary64_12734` `associate-*r/_binary64_12637`
2×	`prod-exp_binary64_12744` `rec-exp_binary64_12745` `associate-/l/_binary64_12642` `frac-2neg_binary64_12706` `pow-prod-down_binary64_12766` `*-commutative_binary64_12626` `distribute-rgt-in_binary64_12645` `1-exp_binary64_12739` `unswap-sqr_binary64_12663` `cbrt-unprod_binary64_12728` `clear-num_binary64_12694` `distribute-lft-in_binary64_12644`
1×	`pow-flip_binary64_12769` `inv-pow_binary64_12780`

Counts

4 → 159

Calls

4 calls:

29.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328) (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z)))
28.0ms	(/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328) (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z))
10.0ms	(.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
8.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))

series278.0ms (4%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328) (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z)))
93.0ms	(/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328) (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z))
42.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
16.0ms	(.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))

simplify156.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4950	9660
1	4950	9660

prune575.0ms (8.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	171	7	178

Error

0.0b

Counts

178 → 7

Compiler

Compiled 9822 to 7110 computations (27.6% saved)

regimes650.0ms (9.4%)

Accuracy

Total 0.7b remaining (96%)

Threshold costs 0.7b (96%)

Compiler

Compiled 6288 to 4860 computations (22.7% saved)

bsearch66.0ms (1%)

Steps

Iters	Range		Point
7	2.875768448437053e+39	1.1325240045234807e+41	1.1146806748453102e+41
10	-1.3027626381252231e+43	-3.602709835585778e+30	-3.361760792985159e+41

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	104	108
1	104	108

end0.0ms (0%)

sample2.0s (28.4%)

Algorithm

1×

intervals

Results

682.0ms	8000×	body	128	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 1738 to 1333 computations (23.3% saved)

Details

analyze936.0ms (13.6%)

sample30.0ms (0.4%)

simplify137.0ms (2%)

prune4.0ms (0.1%)

localize23.0ms (0.3%)

rewrite77.0ms (1.1%)

series214.0ms (3.1%)

simplify88.0ms (1.3%)

prune262.0ms (3.8%)

localize22.0ms (0.3%)

rewrite71.0ms (1%)

series199.0ms (2.9%)

simplify84.0ms (1.2%)

prune265.0ms (3.9%)

localize24.0ms (0.3%)

rewrite69.0ms (1%)

series209.0ms (3%)

simplify100.0ms (1.5%)

prune260.0ms (3.8%)

localize23.0ms (0.3%)

rewrite98.0ms (1.4%)

series278.0ms (4%)

simplify156.0ms (2.3%)

prune575.0ms (8.4%)

regimes650.0ms (9.4%)

bsearch66.0ms (1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.0s (28.4%)

Profiling