Details

analyze412.0ms (5.9%)

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	239×	body	256	valid
3.0ms	39×	body	128	nan
1.0ms	17×	body	128	valid

Compiler

Compiled 75 to 50 computations (33.3% saved)

simplify324.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (227.0ms)

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

Error

39.1b

Counts

2 → 2

Compiler

Compiled 99 to 59 computations (40.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

8.2b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
8.8b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
32.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
32.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_5215`
11×	`cbrt-prod_binary64_5224`
10×	`*-un-lft-identity_binary64_5193`
9×	`sqrt-prod_binary64_5209`
8×	`add-cube-cbrt_binary64_5228`
6×	`times-frac_binary64_5199` `pow1_binary64_5254`
4×	`add-cbrt-cube_binary64_5229` `sqrt-div_binary64_5210` `add-log-exp_binary64_5232` `add-exp-log_binary64_5231` `difference-of-squares_binary64_5162`
2×	`flip3--_binary64_5197` `flip--_binary64_5168` `cbrt-div_binary64_5225` `pow1/2_binary64_5273` `sqrt-pow1_binary64_5211` `rem-sqrt-square_binary64_5206` `pow1/3_binary64_5275`
1×	`distribute-lft-out--_binary64_5145` `associate-*l/_binary64_5136` `div-inv_binary64_5190`

Counts

4 → 61

Calls

4 calls:

9.0ms	(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)))

series564.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
243.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
30.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
28.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5115	1656

prune170.0ms (2.5%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	52	21	73
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	53	22	75

Error

35.2b

Counts

75 → 22

Compiler

Compiled 3604 to 1403 computations (61.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (.f64 g g) (.f64 h h))
8.2b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
32.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
32.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_5215`
10×	`*-un-lft-identity_binary64_5193` `cbrt-prod_binary64_5224`
9×	`sqrt-prod_binary64_5209`
8×	`add-cube-cbrt_binary64_5228`
6×	`add-log-exp_binary64_5232` `times-frac_binary64_5199` `pow1_binary64_5254`
5×	`difference-of-squares_binary64_5162`
4×	`add-cbrt-cube_binary64_5229` `sqrt-div_binary64_5210` `add-exp-log_binary64_5231`
3×	`flip3--_binary64_5197` `flip--_binary64_5168`
2×	`pow1/2_binary64_5273` `sqrt-pow1_binary64_5211` `rem-sqrt-square_binary64_5206`
1×	`distribute-lft-out--_binary64_5145` `sub-neg_binary64_5186` `cbrt-div_binary64_5225` `cancel-sign-sub-inv_binary64_5159` `div-inv_binary64_5190` `diff-log_binary64_5285` `pow1/3_binary64_5275`

Counts

4 → 64

Calls

4 calls:

8.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
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))

series323.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

242.0ms	(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)))
27.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
22.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5010	1501

prune149.0ms (2.2%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	73	25	98

Error

34.1b

Counts

98 → 25

Compiler

Compiled 3836 to 1528 computations (60.2% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (.f64 g g) (.f64 h h))
2.0b	(-.f64 (.f64 g g) (.f64 h h))
32.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
32.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_5232` `sqrt-prod_binary64_5209` `add-sqr-sqrt_binary64_5215`
6×	`add-cube-cbrt_binary64_5228` `*-un-lft-identity_binary64_5193` `pow1_binary64_5254`
4×	`add-cbrt-cube_binary64_5229` `flip3--_binary64_5197` `sqrt-div_binary64_5210` `flip--_binary64_5168` `add-exp-log_binary64_5231` `difference-of-squares_binary64_5162`
2×	`sub-neg_binary64_5186` `pow1/2_binary64_5273` `cancel-sign-sub-inv_binary64_5159` `sqrt-pow1_binary64_5211` `rem-sqrt-square_binary64_5206` `diff-log_binary64_5285`

Counts

4 → 58

Calls

4 calls:

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

series107.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
29.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
26.0ms	(-.f64 (.f64 g g) (.f64 h h))
21.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4931	960
1	4931	960

prune135.0ms (1.9%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	3	21	24
Picked	1	0	1
Done	0	0	0
Total	72	23	95

Error

34.1b

Counts

95 → 23

Compiler

Compiled 3509 to 1405 computations (60% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (.f64 g g) (.f64 h h))
8.8b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
32.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
32.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`sqrt-prod_binary64_5209` `add-sqr-sqrt_binary64_5215`
6×	`add-cube-cbrt_binary64_5228` `add-log-exp_binary64_5232` `*-un-lft-identity_binary64_5193` `pow1_binary64_5254`
4×	`add-cbrt-cube_binary64_5229` `sqrt-div_binary64_5210` `add-exp-log_binary64_5231`
3×	`flip3--_binary64_5197` `flip--_binary64_5168` `difference-of-squares_binary64_5162`
2×	`pow1/2_binary64_5273` `sqrt-pow1_binary64_5211` `rem-sqrt-square_binary64_5206`
1×	`sub-neg_binary64_5186` `cbrt-div_binary64_5225` `associate-*l/_binary64_5136` `cancel-sign-sub-inv_binary64_5159` `cbrt-prod_binary64_5224` `diff-log_binary64_5285` `pow1/3_binary64_5275`

Counts

4 → 55

Calls

4 calls:

8.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
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))

series326.0ms (4.7%)

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))
31.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
28.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
21.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4981	1104
1	4981	1104

prune93.0ms (1.3%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	0	22	22
Picked	1	0	1
Done	0	0	0
Total	64	26	90

Error

34.1b

Counts

90 → 26

Compiler

Compiled 2463 to 859 computations (65.1% saved)

regimes926.0ms (13.4%)

Accuracy

Total 0.6b remaining (2%)

Threshold costs 0.6b (2%)

Compiler

Compiled 14249 to 8209 computations (42.4% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 37 to 23 computations (37.8% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	146	211
1	146	211

end0.0ms (0%)

sample2.9s (41.2%)

Algorithm

1×

intervals

Results

1.2s	7565×	body	256	valid
97.0ms	1221×	body	128	nan
36.0ms	435×	body	128	valid

Compiler

Compiled 2194 to 1249 computations (43.1% saved)

Details

analyze412.0ms (5.9%)

sample56.0ms (0.8%)

simplify324.0ms (4.7%)

prune6.0ms (0.1%)

localize19.0ms (0.3%)

rewrite33.0ms (0.5%)

series564.0ms (8.1%)

simplify64.0ms (0.9%)

prune170.0ms (2.5%)

localize17.0ms (0.2%)

rewrite27.0ms (0.4%)

series323.0ms (4.7%)

simplify80.0ms (1.1%)

prune149.0ms (2.2%)

localize19.0ms (0.3%)

rewrite22.0ms (0.3%)

series107.0ms (1.5%)

simplify81.0ms (1.2%)

prune135.0ms (1.9%)

localize17.0ms (0.3%)

rewrite27.0ms (0.4%)

series326.0ms (4.7%)

simplify69.0ms (1%)

prune93.0ms (1.3%)

regimes926.0ms (13.4%)

bsearch5.0ms (0.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.9s (41.2%)

Profiling