Details

analyze493.0ms

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

sample43.0ms

Algorithm

intervals

Results

9.0ms	32×	body	2560	valid
8.0ms	168×	body	80	valid
5.0ms	23×	body	1280	valid
4.0ms	22×	body	640	valid
3.0ms	17×	body	80	invalid
2.0ms	36×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	5×	body	160	valid

simplify220.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (217.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	16

prune6.0ms

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: 34.1b

Counts

2 → 1

localize11.0ms

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))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 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:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.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)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
16.0ms	(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

prune91.0ms

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: 4.6b

Counts

83 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
2.8b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
9.6b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
23.5b	(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))
14.0ms	(/.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)))

series139.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
48.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
66.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
15.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4931	2022
1	4931	2022

prune85.0ms

Filtered

75 candidates to 113 candidates (-50.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	113	8	121

Merged error: 4.6b

Counts

121 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4 a) c)
0.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

5.0ms	(.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))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (.f64 4 a) c)
16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
15.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4941	746
1	4941	746

prune54.0ms

Filtered

48 candidates to 68 candidates (-41.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	68	8	76

Merged error: 4.3b

Counts

76 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))))
0.5b	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
1.8b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
23.5b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
18×	`associate-r_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
10×	`pow1_binary64`
8×	`add-log-exp_binary64`
6×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`flip3-+_binary64` `distribute-lft-out_binary64` `flip-+_binary64`
3×	`pow-prod-down_binary64` `sqrt-prod_binary64`
2×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `+-commutative_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `associate-r/_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 76

Calls

4 calls:

14.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))))
6.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))))
18.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
9.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
16.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

simplify41.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4961	1254
1	4961	1254

prune53.0ms

Filtered

64 candidates to 88 candidates (-37.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	88	8	96

Merged error: 4.3b

Counts

96 → 8

regimes200.0ms

Accuracy

93.1% (1.7b remaining)

Error of 7.3b against oracle of 5.7b and baseline of 29.9b

bsearch53.0ms

Steps

Iters	Range		Point
1	1.0222296758689803e+121	1.0910113803129012e+121	1.0321611733451932e+121
8	-1.6886234969069345e-297	-7.188044641578526e-301	-4.61052798615193e-299
9	-112243332068.72598	-89552.36570462812	-110883243782.23416

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	107	57
1	107	57

end0.0ms

sample1.3s

Algorithm

intervals

Results

349.0ms	1096×	body	2560	valid
281.0ms	5154×	body	80	valid
234.0ms	917×	body	1280	valid
89.0ms	423×	body	640	valid
37.0ms	710×	body	80	nan
35.0ms	217×	body	320	valid
34.0ms	88×	body	5120	valid
19.0ms	357×	body	80	invalid
14.0ms	105×	body	160	valid

Details

analyze493.0ms

sample43.0ms

simplify220.0ms

prune6.0ms

localize11.0ms

rewrite34.0ms

series70.0ms

simplify61.0ms

prune91.0ms

localize15.0ms

rewrite42.0ms

series139.0ms

simplify57.0ms

prune85.0ms

localize12.0ms

rewrite22.0ms

series44.0ms

simplify48.0ms

prune54.0ms

localize10.0ms

rewrite32.0ms

series97.0ms

simplify41.0ms

prune53.0ms

regimes200.0ms

bsearch53.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling