Details

analyze431.0ms (6.1%)

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
12.5%	68.6%	18.9%	6
18.7%	62.4%	18.9%	7
18.7%	59.3%	22%	8
28.1%	39%	32.9%	9
32.8%	34.3%	32.9%	10
32.8%	32%	35.3%	11
38.2%	20.7%	41.1%	12
41%	17.9%	41.1%	13
41%	16.6%	42.5%	14

Compiler

Compiled 38 to 24 computations (36.8% saved)

sample56.0ms (0.8%)

Algorithm

1×

intervals

Results

40.0ms	242×	body	256	valid
3.0ms	39×	body	128	nan
1.0ms	14×	body	128	valid

Compiler

Compiled 75 to 50 computations (33.3% saved)

simplify331.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (231.0ms)

Iter	Nodes	Cost
0	4834	48
1	4834	48

prune6.0ms (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

Merged error: 36.6b

Counts

2 → 2

Compiler

Compiled 99 to 59 computations (40.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.4b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
7.6b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2487`
11×	`cbrt-prod_binary64_2496`
10×	`*-un-lft-identity_binary64_2465`
9×	`sqrt-prod_binary64_2481`
8×	`add-cube-cbrt_binary64_2500`
6×	`times-frac_binary64_2471` `pow1_binary64_2526`
4×	`difference-of-squares_binary64_2434` `add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482`
2×	`flip--_binary64_2440` `pow1/2_binary64_2545` `cbrt-div_binary64_2497` `pow1/3_binary64_2547` `rem-sqrt-square_binary64_2478` `flip3--_binary64_2469` `sqrt-pow1_binary64_2483`
1×	`associate-*l/_binary64_2408` `distribute-lft-out--_binary64_2417` `div-inv_binary64_2462`

Counts

4 → 61

Calls

4 calls:

12.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
9.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series548.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

245.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
245.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
29.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
28.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5115	1656

prune166.0ms (2.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	56	17	73
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	57	18	75

Merged error: 33.0b

Counts

75 → 18

Compiler

Compiled 3494 to 1322 computations (62.2% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.4b	(-.f64 (.f64 g g) (.f64 h h))
6.4b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2487`
10×	`*-un-lft-identity_binary64_2465` `cbrt-prod_binary64_2496`
9×	`sqrt-prod_binary64_2481`
8×	`add-cube-cbrt_binary64_2500`
6×	`add-log-exp_binary64_2504` `times-frac_binary64_2471` `pow1_binary64_2526`
5×	`difference-of-squares_binary64_2434`
4×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482`
3×	`flip--_binary64_2440` `flip3--_binary64_2469`
2×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`
1×	`cbrt-div_binary64_2497` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `pow1/3_binary64_2547` `cancel-sign-sub-inv_binary64_2431` `div-inv_binary64_2462` `diff-log_binary64_2557`

Counts

4 → 64

Calls

4 calls:

9.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
5.0ms	(-.f64 (.f64 g g) (.f64 h h))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series327.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
32.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
28.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
24.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5010	1501

prune151.0ms (2.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	73	21	94

Merged error: 31.9b

Counts

94 → 21

Compiler

Compiled 3740 to 1446 computations (61.3% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.4b	(-.f64 (.f64 g g) (.f64 h h))
2.4b	(-.f64 (.f64 g g) (.f64 h h))
30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_2504` `sqrt-prod_binary64_2481` `add-sqr-sqrt_binary64_2487`
6×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526`
4×	`difference-of-squares_binary64_2434` `flip--_binary64_2440` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482` `flip3--_binary64_2469`
2×	`pow1/2_binary64_2545` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `sqrt-pow1_binary64_2483`

Counts

4 → 58

Calls

4 calls:

6.0ms	(-.f64 (.f64 g g) (.f64 h h))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))

series106.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
25.0ms	(-.f64 (.f64 g g) (.f64 h h))
25.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4931	960
1	4931	960

prune129.0ms (1.8%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	20	20
Picked	1	0	1
Done	0	0	0
Total	69	22	91

Merged error: 31.9b

Counts

91 → 22

Compiler

Compiled 3516 to 1383 computations (60.7% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`sqrt-prod_binary64_2481`
12×	`add-sqr-sqrt_binary64_2487`
8×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526` `sqrt-div_binary64_2482`
4×	`difference-of-squares_binary64_2434` `add-log-exp_binary64_2504` `flip--_binary64_2440` `pow1/2_binary64_2545` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `rem-sqrt-square_binary64_2478` `flip3--_binary64_2469` `sqrt-pow1_binary64_2483`

Counts

4 → 64

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series112.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
28.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
26.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5037	1068

prune126.0ms (1.8%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	2	19	21
Picked	0	1	1
Done	0	0	0
Total	75	23	98

Merged error: 31.9b

Counts

98 → 23

Compiler

Compiled 4728 to 1031 computations (78.2% saved)

regimes1.1s (15%)

Compiler: Compiled 13857 to 7726 computations (44.2% saved)

bsearch162.0ms (2.3%)

Steps

Iters	Range		Point
8	2.590301150334571e-132	1.4861873965707086e-127	1.037351012381759e-131
12	-3.188004767728901e-118	-1.0469129648288081e-165	-7.035285471056203e-159

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	193
1	83	193

end0.0ms (0%)

sample2.9s (40.7%)

Algorithm

1×

intervals

Results

1.3s	7565×	body	256	valid
106.0ms	1252×	body	128	nan
38.0ms	435×	body	128	valid

Compiler

Compiled 2126 to 1165 computations (45.2% saved)

Details

analyze431.0ms (6.1%)

sample56.0ms (0.8%)

simplify331.0ms (4.7%)

prune6.0ms (0.1%)

localize18.0ms (0.3%)

rewrite38.0ms (0.5%)

series548.0ms (7.7%)

simplify58.0ms (0.8%)

prune166.0ms (2.3%)

localize22.0ms (0.3%)

rewrite31.0ms (0.4%)

series327.0ms (4.6%)

simplify76.0ms (1.1%)

prune151.0ms (2.1%)

localize20.0ms (0.3%)

rewrite26.0ms (0.4%)

series106.0ms (1.5%)

simplify77.0ms (1.1%)

prune129.0ms (1.8%)

localize30.0ms (0.4%)

rewrite28.0ms (0.4%)

series112.0ms (1.6%)

simplify67.0ms (0.9%)

prune126.0ms (1.8%)

regimes1.1s (15%)

bsearch162.0ms (2.3%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.9s (40.7%)

Profiling