Details

analyze431.0ms (6.2%)

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)

sample59.0ms (0.8%)

Algorithm

1×

intervals

Results

43.0ms	241×	body	256	valid
3.0ms	36×	body	128	nan
1.0ms	15×	body	128	valid

Compiler

Compiled 75 to 50 computations (33.3% saved)

simplify209.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (202.0ms)

Iter	Nodes	Cost
0	4882	48
1	4882	48

prune7.0ms (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: 33.8b

Counts

2 → 2

Compiler

Compiled 99 to 59 computations (40.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.2b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
9.4b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
27.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
9×	`sqrt-prod_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
2×	`cbrt-div_binary64` `pow1/2_binary64` `flip3--_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`distribute-lft-out--_binary64` `div-inv_binary64` `associate-*l/_binary64`

Counts

4 → 61

Calls

4 calls:

13.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
9.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series1.0s (14.8%)

Counts

4 → 12

Calls

4 calls:

463.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
458.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
58.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
56.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4980	1656
1	4980	1656

prune172.0ms (2.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	55	18	73
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	56	19	75

Merged error: 29.4b

Counts

75 → 19

Compiler

Compiled 3520 to 1338 computations (62% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.6b	(-.f64 (.f64 g g) (.f64 h h))
8.2b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
27.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-div_binary64` `sub-neg_binary64` `diff-log_binary64` `pow1/3_binary64` `cbrt-prod_binary64` `associate-*l/_binary64`

Counts

4 → 54

Calls

4 calls:

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

series618.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

457.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
62.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
56.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
44.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4975	1095
1	4975	1095

prune142.0ms (2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	64	21	85

Merged error: 28.2b

Counts

85 → 21

Compiler

Compiled 3274 to 1307 computations (60.1% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

2.6b	(-.f64 (.f64 g g) (.f64 h h))
2.6b	(-.f64 (.f64 g g) (.f64 h h))
27.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
6×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 56

Calls

4 calls:

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

series215.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
58.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
51.0ms	(-.f64 (.f64 g g) (.f64 h h))
42.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5177	948

prune138.0ms (2%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	20	20
Picked	0	1	1
Done	0	0	0
Total	65	24	89

Merged error: 28.2b

Counts

89 → 24

Compiler

Compiled 3484 to 1386 computations (60.2% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.6b	(-.f64 (.f64 g g) (.f64 h h))
8.2b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
27.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-div_binary64` `sub-neg_binary64` `diff-log_binary64` `pow1/3_binary64` `cbrt-prod_binary64` `associate-*l/_binary64`

Counts

4 → 54

Calls

4 calls:

10.0ms	(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)))
5.0ms	(-.f64 (.f64 g g) (.f64 h h))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series610.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

455.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
59.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
54.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
42.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4975	1095
1	4975	1095

prune96.0ms (1.4%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	2	20	22
Picked	1	0	1
Done	0	1	1
Total	65	25	90

Merged error: 28.2b

Counts

90 → 25

Compiler

Compiled 2428 to 851 computations (65% saved)

regimes486.0ms (7%)

Compiler: Compiled 7291 to 3925 computations (46.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	52
1	51	52

end0.0ms (0%)

sample2.3s (33%)

Algorithm

1×

intervals

Results

1.3s	7615×	body	256	valid
98.0ms	1189×	body	128	nan
35.0ms	385×	body	128	valid

Compiler

Compiled 1098 to 594 computations (45.9% saved)

Details

analyze431.0ms (6.2%)

sample59.0ms (0.8%)

simplify209.0ms (3%)

prune7.0ms (0.1%)

localize17.0ms (0.2%)

rewrite38.0ms (0.6%)

series1.0s (14.8%)

simplify55.0ms (0.8%)

prune172.0ms (2.5%)

localize18.0ms (0.3%)

rewrite30.0ms (0.4%)

series618.0ms (8.9%)

simplify72.0ms (1%)

prune142.0ms (2%)

localize25.0ms (0.4%)

rewrite25.0ms (0.4%)

series215.0ms (3.1%)

simplify56.0ms (0.8%)

prune138.0ms (2%)

localize19.0ms (0.3%)

rewrite30.0ms (0.4%)

series610.0ms (8.7%)

simplify73.0ms (1%)

prune96.0ms (1.4%)

regimes486.0ms (7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (33%)

Profiling