Details

analyze457.0ms

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample44.0ms

Algorithm

intervals

Results

10.0ms	167×	body	80	valid
9.0ms	30×	body	2560	valid
7.0ms	30×	body	1280	valid
3.0ms	17×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	22×	body	80	nan
1.0ms	5×	body	320	valid
1.0ms	12×	body	80	invalid
0.0ms	3×	body	160	valid

simplify214.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (212.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	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: 38.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite31.0ms

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 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
21.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
13.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4900	1294
1	4900	1294

prune122.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 7.6b

Counts

83 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
3.4b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.6b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
4×	`distribute-lft-out_binary64` `div-inv_binary64`
3×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_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 → 101

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
55.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
77.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4931	2022
1	4931	2022

prune120.0ms

Filtered

75 candidates to 113 candidates (-50.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	115	6	121

Merged error: 7.5b

Counts

121 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series114.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
20.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4887	1292
1	4887	1292

prune94.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	83	6	89

Merged error: 7.5b

Counts

89 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
3.4b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 c -4) (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (*.f64 a 2))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
28×	`cbrt-undiv_binary64` `div-exp_binary64`
23×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`sqrt-div_binary64`
3×	`associate-/l/_binary64` `flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 85

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
25.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 c -4) (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (*.f64 a 2))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
64.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 c -4) (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (*.f64 a 2))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4953	2098
1	4953	2098

prune92.0ms

Filtered

59 candidates to 97 candidates (-64.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	97	6	103

Merged error: 7.5b

Counts

103 → 6

regimes241.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.8b

bsearch80.0ms

Steps

Iters	Range	Point
6	1.5254191584927803e+91	1.9406410536970233e+92	2.4801938863971876e+91
8	-8.878839583541517e-240	-5.411190655501986e-243	-2.6603754368549326e-241
8	-3.476586232975515e+112	-9.977119098877996e+107	-5.948493915058576e+108

Iters

Range

Point

1.5254191584927803e+91

1.9406410536970233e+92

2.4801938863971876e+91

-8.878839583541517e-240

-5.411190655501986e-243

-2.6603754368549326e-241

-3.476586232975515e+112

-9.977119098877996e+107

-5.948493915058576e+108

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	103	55
1	103	55

end0.0ms

sample1.3s

Algorithm

intervals

Results

319.0ms	1039×	body	2560	valid
269.0ms	5148×	body	80	valid
221.0ms	919×	body	1280	valid
91.0ms	460×	body	640	valid
42.0ms	106×	body	5120	valid
36.0ms	230×	body	320	valid
35.0ms	671×	body	80	nan
21.0ms	396×	body	80	invalid
9.0ms	98×	body	160	valid

Details

analyze457.0ms

sample44.0ms

simplify214.0ms

prune7.0ms

localize10.0ms

rewrite31.0ms

series86.0ms

simplify61.0ms

prune122.0ms

localize14.0ms

rewrite42.0ms

series163.0ms

simplify52.0ms

prune120.0ms

localize12.0ms

rewrite28.0ms

series114.0ms

simplify67.0ms

prune94.0ms

localize17.0ms

rewrite44.0ms

series117.0ms

simplify61.0ms

prune92.0ms

regimes241.0ms

bsearch80.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling