Details

analyze453.0ms

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample43.0ms

Algorithm

intervals

Results

11.0ms	37×	body	2560	valid
8.0ms	166×	body	80	valid
5.0ms	20×	body	1280	valid
4.0ms	20×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	22×	body	80	nan
1.0ms	7×	body	320	valid
1.0ms	12×	body	80	invalid
0.0ms	2×	body	160	valid

simplify221.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (219.0ms)

Iter	Nodes	Cost
0	1801	16
1	1801	16

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 36.7b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
26.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
19.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4895	1297
1	4895	1297

prune126.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 5.2b

Counts

83 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) a))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
26.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
22×	`associate-r_binary64`
19×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `difference-of-squares_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
4×	`distribute-lft-out--_binary64`
3×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

14.0ms	(.f64 1/3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) a))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(.f64 1/3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) a))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
20.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4925	1433
1	4925	1433

prune108.0ms

Filtered

66 candidates to 93 candidates (-40.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	92	10	102

Merged error: 5.2b

Counts

102 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/3 a)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
26.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`sqrt-prod_binary64`
3×	`associate-/r_binary64` `flip3--_binary64` `associate-/l_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 67

Calls

4 calls:

3.0ms	(/.f64 1/3 a)
7.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/.f64 1/3 a)
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
19.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5069	856

prune94.0ms

Filtered

60 candidates to 79 candidates (-31.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	79	10	89

Merged error: 5.1b

Counts

89 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
26.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
6×	`add-cube-cbrt_binary64`
4×	`sqrt-prod_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(.f64 (.f64 3 a) c)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(.f64 (.f64 3 a) c)
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
19.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
21.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5400	804

prune57.0ms

Filtered

49 candidates to 70 candidates (-42.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	70	10	80

Merged error: 5.1b

Counts

80 → 10

regimes500.0ms

Accuracy

84% (4.6b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 34.5b

bsearch62.0ms

Steps

Iters	Range		Point
11	3.985338653952686e-49	1.636968041454199e-16	1.8863642337546708e-35
8	-3.81136999452096e+119	-1.2103101912761451e+117	-1.722835689509259e+119

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	109	40
1	109	40

end0.0ms

sample1.3s

Algorithm

intervals

Results

310.0ms	1048×	body	2560	valid
268.0ms	5111×	body	80	valid
231.0ms	924×	body	1280	valid
93.0ms	494×	body	640	valid
41.0ms	106×	body	5120	valid
35.0ms	670×	body	80	nan
34.0ms	224×	body	320	valid
20.0ms	395×	body	80	invalid
9.0ms	93×	body	160	valid

Details

analyze453.0ms

sample43.0ms

simplify221.0ms

prune7.0ms

localize10.0ms

rewrite34.0ms

series86.0ms

simplify74.0ms

prune126.0ms

localize12.0ms

rewrite34.0ms

series86.0ms

simplify58.0ms

prune108.0ms

localize11.0ms

rewrite24.0ms

series53.0ms

simplify49.0ms

prune94.0ms

localize10.0ms

rewrite24.0ms

series56.0ms

simplify44.0ms

prune57.0ms

regimes500.0ms

bsearch62.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling