Details

analyze432.0ms

Algorithm

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

sample67.0ms

Algorithm

intervals

Results

31.0ms	119×	body	320	valid
22.0ms	135×	body	160	valid
3.0ms	41×	body	80	nan
0.0ms	2×	body	80	valid

simplify185.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (182.0ms)

Iter	Nodes	Cost
0	4925	31
1	4925	31

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 39.1b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

9.6b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
9.6b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
31.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite29.0ms

Algorithm

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:

9.0ms	(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)))

series140.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
60.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
8.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
10.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify50.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4911	1064
1	4911	1064

prune126.0ms

Filtered

63 candidates to 73 candidates (-15.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	59	14	73
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	61	14	75

Merged error: 33.4b

Counts

75 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

4.0b	(-.f64 (.f64 g g) (.f64 h h))
9.6b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
31.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite25.0ms

Algorithm

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:

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

series84.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 (.f64 g g) (.f64 h h))
62.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
8.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
8.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify47.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4972	716
1	4972	716

prune86.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	67	13	80

Merged error: 33.0b

Counts

80 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

4.0b	(-.f64 (.f64 g g) (.f64 h h))
4.0b	(-.f64 (.f64 g g) (.f64 h h))
31.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite20.0ms

Algorithm

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

series28.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(-.f64 (.f64 g g) (.f64 h h))
6.0ms	(-.f64 (.f64 g g) (.f64 h h))
8.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
8.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify55.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4920	632
1	4920	632

prune86.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	66	15	81

Merged error: 33.0b

Counts

81 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

4.0b	(-.f64 (.f64 g g) (.f64 h h))
9.6b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
31.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite25.0ms

Algorithm

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:

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

series85.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 (.f64 g g) (.f64 h h))
63.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
8.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
8.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify48.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4972	716
1	4972	716

prune50.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	14	14
Picked	1	0	1
Done	0	0	0
Total	65	16	81

Merged error: 33.0b

Counts

81 → 16

Details

analyze432.0ms

sample67.0ms

simplify185.0ms

prune8.0ms

localize16.0ms

rewrite29.0ms

series140.0ms

simplify50.0ms

prune126.0ms

localize18.0ms

rewrite25.0ms

series84.0ms

simplify47.0ms

prune86.0ms

localize19.0ms

rewrite20.0ms

series28.0ms

simplify55.0ms

prune86.0ms

localize21.0ms

rewrite25.0ms

series85.0ms

simplify48.0ms

prune50.0ms

regimes308.0ms

bsearch14.0ms

Profiling