Details

analyze1.0s (14.3%)

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)

sample31.0ms (0.4%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify48.0ms (0.7%)

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

Merged error: 27.2b

Counts

2 → 1

Compiler

Compiled 74 to 58 computations (21.6% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)
0.0b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
0.1b	(.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
26.2b	(/.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))

rewrite84.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
8×	`associate-/l/_binary64` `associate-*l/_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `flip3--_binary64` `unswap-sqr_binary64` `times-frac_binary64` `flip--_binary64` `-commutative_binary64`
2×	`cbrt-undiv_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `div-exp_binary64`
1×	`clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 91

Calls

4 calls:

37.0ms	(/.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))
12.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
11.0ms	(.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)
8.0ms	(.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)

series414.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

283.0ms	(/.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))
74.0ms	(.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
30.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
27.0ms	(.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5453	3045

prune762.0ms (10.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Merged error: 0.0b

Counts

104 → 8

Compiler

Compiled 16942 to 12802 computations (24.4% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
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))
25.3b	(/.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))

rewrite80.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64` `associate-l_binary64` `times-frac_binary64`
6×	`associate-*r/_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 97

Calls

4 calls:

32.0ms	(/.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))
12.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
12.0ms	(.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
8.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))

series389.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

250.0ms	(/.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))
81.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
32.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
26.0ms	(.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))

simplify95.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4960	3372
1	4960	3372

prune363.0ms (5.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	108	9	117

Merged error: 0.0b

Counts

117 → 9

Compiler

Compiled 7820 to 5753 computations (26.4% saved)

localize28.0ms (0.4%)

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))
0.1b	(.f64 x (.f64 x (+.f64 x 6099563062176297/140737488355328)))
25.3b	(/.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))

rewrite76.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`pow1_binary64`
9×	`associate-l_binary64` `times-frac_binary64`
8×	`associate-*r/_binary64`
7×	`associate-r_binary64`
6×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
5×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 99

Calls

4 calls:

33.0ms	(/.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))
12.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
9.0ms	(.f64 x (.f64 x (+.f64 x 6099563062176297/140737488355328)))
8.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))

series603.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

422.0ms	(/.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))
77.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
67.0ms	(.f64 x (.f64 x (+.f64 x 6099563062176297/140737488355328)))
36.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))

simplify98.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4975	3283
1	4975	3283

prune313.0ms (4.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	112	8	120

Merged error: 0.0b

Counts

120 → 8

Compiler

Compiled 6600 to 4761 computations (27.9% saved)

localize26.0ms (0.4%)

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))
0.1b	(.f64 (.f64 x x) (+.f64 x 6099563062176297/140737488355328))
25.3b	(/.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 (.f64 x x) (+.f64 x 6099563062176297/140737488355328)) (.f64 x 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))

rewrite81.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`pow1_binary64`
10×	`associate-r_binary64`
9×	`times-frac_binary64`
7×	`associate-l_binary64`
6×	`associate-*r/_binary64`
5×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`distribute-lft-out_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 99

Calls

4 calls:

35.0ms	(/.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 (.f64 x x) (+.f64 x 6099563062176297/140737488355328)) (.f64 x 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
12.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
9.0ms	(.f64 (.f64 x x) (+.f64 x 6099563062176297/140737488355328))
8.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))

series398.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

230.0ms	(/.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 (.f64 x x) (+.f64 x 6099563062176297/140737488355328)) (.f64 x 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
72.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
65.0ms	(.f64 (.f64 x x) (+.f64 x 6099563062176297/140737488355328))
30.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))

simplify95.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4923	3290
1	4923	3290

prune254.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	111	8	119

Merged error: 0.0b

Counts

119 → 8

Compiler

Compiled 5362 to 3710 computations (30.8% saved)

regimes288.0ms (4.1%)

Compiler: Compiled 1080 to 864 computations (20% saved)

bsearch74.0ms (1.1%)

Steps

Iters	Range		Point
8	2.3626216854607965e+33	6.76773710210592e+37	4.681623202233483e+37
10	-4.2949925276713654e+48	-1.0868566420419711e+30	-6.808458039899931e+39

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	114
1	89	114

end0.0ms (0%)

sample1.3s (18%)

Algorithm

1×

intervals

Results

696.0ms	8000×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 548 to 423 computations (22.8% saved)

Details

analyze1.0s (14.3%)

sample31.0ms (0.4%)

simplify48.0ms (0.7%)

prune4.0ms (0.1%)

localize24.0ms (0.3%)

rewrite84.0ms (1.2%)

series414.0ms (5.9%)

simplify82.0ms (1.2%)

prune762.0ms (10.9%)

localize26.0ms (0.4%)

rewrite80.0ms (1.1%)

series389.0ms (5.6%)

simplify95.0ms (1.4%)

prune363.0ms (5.2%)

localize28.0ms (0.4%)

rewrite76.0ms (1.1%)

series603.0ms (8.6%)

simplify98.0ms (1.4%)

prune313.0ms (4.5%)

localize26.0ms (0.4%)

rewrite81.0ms (1.2%)

series398.0ms (5.7%)

simplify95.0ms (1.4%)

prune254.0ms (3.6%)

regimes288.0ms (4.1%)

bsearch74.0ms (1.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.3s (18%)

Profiling