Details

analyze408.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample43.0ms

Algorithm

intervals

Results

10.0ms	37×	body	2560	valid
7.0ms	161×	body	80	valid
5.0ms	23×	body	1280	valid
4.0ms	3×	body	5120	valid
3.0ms	18×	body	640	valid
1.0ms	32×	body	80	nan
1.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	3×	body	80	invalid

simplify489.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	713	13
1	713	13

prune5.0ms

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: 36.2b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
1.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 89

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
13.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
13.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
27.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5012	1566

prune131.0ms

Filtered

73 candidates to 101 candidates (-38.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	8	102

Merged error: 6.2b

Counts

102 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
5.2b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
10.9b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
15.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
13.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series138.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
50.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
61.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
19.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4961	2482
1	4961	2482

prune132.0ms

Filtered

103 candidates to 135 candidates (-31.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Merged error: 6.2b

Counts

143 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

13.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series102.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
16.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4902	1364
1	4902	1364

prune95.0ms

Filtered

71 candidates to 93 candidates (-31.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	93	8	101

Merged error: 6.2b

Counts

101 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_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 → 52

Calls

4 calls:

5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
16.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
16.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5275	660

prune59.0ms

Filtered

52 candidates to 64 candidates (-23.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	64	8	72

Merged error: 6.2b

Counts

72 → 8

regimes295.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.6b

bsearch72.0ms

Steps

Iters	Range	Point
6	7.621631647479164e+54	1.1620003065684158e+56	8.146902378104984e+55
9	-7.69721194200277e-282	-3.897062007467286e-287	-3.9422997567625006e-287
7	-6.383117637049118e+125	-1.5564611129376612e+124	-5.882030433389928e+125

Iters

Range

Point

7.621631647479164e+54

1.1620003065684158e+56

8.146902378104984e+55

-7.69721194200277e-282

-3.897062007467286e-287

-3.9422997567625006e-287

-6.383117637049118e+125

-1.5564611129376612e+124

-5.882030433389928e+125

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	179	54
1	179	54

end0.0ms

sample1.1s

Algorithm

intervals

Results

272.0ms	1114×	body	2560	valid
218.0ms	5045×	body	80	valid
180.0ms	903×	body	1280	valid
76.0ms	479×	body	640	valid
35.0ms	831×	body	80	nan
32.0ms	108×	body	5120	valid
30.0ms	242×	body	320	valid
13.0ms	308×	body	80	invalid
9.0ms	109×	body	160	valid

Details

analyze408.0ms

sample43.0ms

simplify489.0ms

prune5.0ms

localize12.0ms

rewrite48.0ms

series69.0ms

simplify65.0ms

prune131.0ms

localize10.0ms

rewrite43.0ms

series138.0ms

simplify67.0ms

prune132.0ms

localize10.0ms

rewrite35.0ms

series102.0ms

simplify39.0ms

prune95.0ms

localize15.0ms

rewrite22.0ms

series47.0ms

simplify49.0ms

prune59.0ms

regimes295.0ms

bsearch72.0ms

simplify4.0ms

end0.0ms

sample1.1s

Profiling