Details

analyze3.8s (1.3%)

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
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample186.0ms (0.1%)

Algorithm

1×

intervals

Results

103.0ms	256×	body	128	valid
4.0ms	24×	body	128	nan
1.0ms	4×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify2.4s (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.9s)

Iter	Nodes	Cost
0	4219	54
1	4219	54

prune54.0ms (0%)

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: 20.4b

Counts

2 → 2

Compiler

Compiled 110 to 76 computations (30.9% saved)

localize214.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite208.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
11×	`*-un-lft-identity_binary64_78`
8×	`add-log-exp_binary64_117`
7×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113`
6×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `difference-of-squares_binary64_47` `pow1/2_binary64_158`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `distribute-lft-out--_binary64_30` `diff-log_binary64_170` `distribute-lft-out_binary64_29` `sub-neg_binary64_71` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 59

Calls

4 calls:

65.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
33.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
33.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series2.2s (0.7%)

Counts

4 → 12

Calls

4 calls:

654.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
630.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
505.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
407.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify510.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (408.0ms)

Iter	Nodes	Cost
0	4936	1457
1	4936	1457

prune2.5s (0.9%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	46	25	71
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	48	25	73

Merged error: 8.9b

Counts

73 → 25

Compiler

Compiled 4229 to 2613 computations (38.2% saved)

localize141.0ms (0%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.2b	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) (neg.f64 b))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite51.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_78`
10×	`add-log-exp_binary64_117`
8×	`add-sqr-sqrt_binary64_100`
6×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `sqrt-div_binary64_95`
3×	`distribute-lft-out_binary64_29` `sum-log_binary64_169`
2×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `flip--_binary64_53` `pow1/2_binary64_158` `flip3-+_binary64_81`
1×	`associate-+r-_binary64_12` `neg-sub0_binary64_73` `unsub-neg_binary64_72` `distribute-rgt-neg-in_binary64_36` `neg-log_binary64_171`

Counts

4 → 58

Calls

4 calls:

17.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) (neg.f64 b))
12.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series1.8s (0.6%)

Counts

4 → 12

Calls

4 calls:

655.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
543.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
451.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
153.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) (neg.f64 b))

simplify606.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (474.0ms)

Iter	Nodes	Cost
0	5095	1410

prune3.7s (1.3%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	55	15	70
Fresh	7	17	24
Picked	0	1	1
Done	0	0	0
Total	62	33	95

Merged error: 8.9b

Counts

95 → 33

Compiler

Compiled 4564 to 2823 computations (38.1% saved)

localize230.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.2b	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) (neg.f64 b))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite276.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_78`
10×	`add-log-exp_binary64_117`
8×	`add-sqr-sqrt_binary64_100`
6×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `sqrt-div_binary64_95`
3×	`distribute-lft-out_binary64_29` `sum-log_binary64_169`
2×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `flip--_binary64_53` `pow1/2_binary64_158` `flip3-+_binary64_81`
1×	`associate-+r-_binary64_12` `neg-sub0_binary64_73` `unsub-neg_binary64_72` `distribute-rgt-neg-in_binary64_36` `neg-log_binary64_171`

Counts

4 → 58

Calls

4 calls:

101.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) (neg.f64 b))
59.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
54.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
52.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series1.8s (0.6%)

Counts

4 → 12

Calls

4 calls:

594.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
539.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) (neg.f64 b))
392.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
277.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify730.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (599.0ms)

Iter	Nodes	Cost
0	5095	1410

prune4.2s (1.4%)

Pruning

44 alts after pruning (43 fresh and 1 done)

	Pruned	Kept	Total
New	52	18	70
Fresh	6	25	31
Picked	1	0	1
Done	0	1	1
Total	59	44	103

Merged error: 8.9b

Counts

103 → 44

Compiler

Compiled 5264 to 3362 computations (36.1% saved)

localize221.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite185.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
11×	`*-un-lft-identity_binary64_78`
8×	`add-log-exp_binary64_117`
7×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113`
6×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `difference-of-squares_binary64_47` `pow1/2_binary64_158`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `distribute-lft-out--_binary64_30` `diff-log_binary64_170` `distribute-lft-out_binary64_29` `sub-neg_binary64_71` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 59

Calls

4 calls:

60.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
47.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
41.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
30.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series1.4s (0.5%)

Counts

4 → 12

Calls

4 calls:

562.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
299.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
280.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
275.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify848.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (689.0ms)

Iter	Nodes	Cost
0	4936	1457
1	4936	1457

prune4.9s (1.7%)

Pruning

58 alts after pruning (58 fresh and 0 done)

	Pruned	Kept	Total
New	48	23	71
Fresh	7	35	42
Picked	1	0	1
Done	1	0	1
Total	57	58	115

Merged error: 8.9b

Counts

115 → 58

Compiler

Compiled 3284 to 2061 computations (37.2% saved)

regimes29.3s (10%)

Compiler: Compiled 37550 to 26626 computations (29.1% saved)

bsearch3.2min (64.3%)

Compiler: Compiled 38 to 26 computations (31.6% saved)

simplify143.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	154	499
1	154	499

end0.0ms (0%)

sample42.3s (14.4%)

Algorithm

1×

intervals

Results

2.6s	8000×	body	128	valid
260.0ms	698×	body	128	nan
112.0ms	389×	body	128	invalid

Compiler

Compiled 11584 to 8029 computations (30.7% saved)

Pareto

0.101955342637129

Details

analyze3.8s (1.3%)

sample186.0ms (0.1%)

simplify2.4s (0.8%)

prune54.0ms (0%)

localize214.0ms (0.1%)

rewrite208.0ms (0.1%)

series2.2s (0.7%)

simplify510.0ms (0.2%)

prune2.5s (0.9%)

localize141.0ms (0%)

rewrite51.0ms (0%)

series1.8s (0.6%)

simplify606.0ms (0.2%)

prune3.7s (1.3%)

localize230.0ms (0.1%)

rewrite276.0ms (0.1%)

series1.8s (0.6%)

simplify730.0ms (0.2%)

prune4.2s (1.4%)

localize221.0ms (0.1%)

rewrite185.0ms (0.1%)

series1.4s (0.5%)

simplify848.0ms (0.3%)

prune4.9s (1.7%)

regimes29.3s (10%)

bsearch3.2min (64.3%)

simplify143.0ms (0%)

end0.0ms (0%)

sample42.3s (14.4%)

Profiling