Details

analyze469.0ms

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

sample44.0ms

Algorithm

intervals

Results

10.0ms	33×	body	2560	valid
9.0ms	165×	body	80	valid
8.0ms	31×	body	1280	valid
2.0ms	5×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	28×	body	80	nan
1.0ms	9×	body	320	valid
1.0ms	16×	body	80	invalid
0.0ms	4×	body	160	valid

simplify210.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (208.0ms)

Iter	Nodes	Cost
0	1801	16
1	1801	16

prune8.0ms

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: 35.7b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
26.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite30.0ms

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:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
4.0ms	(-.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)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4895	1297
1	4895	1297

prune91.0ms

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: 6.1b

Counts

83 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.6b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
9.9b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
26.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
21×	`*-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` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`sqrt-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 102

Calls

4 calls:

8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
14.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
11.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series144.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
46.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
66.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify36.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4955	2125
1	4955	2125

prune91.0ms

Filtered

77 candidates to 114 candidates (-48.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	114	9	123

Merged error: 6.0b

Counts

123 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 1/3 (.f64 1 (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
26.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
15×	`prod-exp_binary64`
10×	`pow1_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
4×	`div-exp_binary64`
3×	`pow-prod-down_binary64` `1-exp_binary64` `associate-l_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 64

Calls

4 calls:

13.0ms	(.f64 1/3 (.f64 1 (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(.f64 1/3 (.f64 1 (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4902	1041
1	4902	1041

prune65.0ms

Filtered

54 candidates to 76 candidates (-40.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	75	10	85

Merged error: 6.0b

Counts

85 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
26.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 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 3 a) c)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (.f64 3 a) c)
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify30.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4965	748
1	4965	748

prune53.0ms

Filtered

48 candidates to 68 candidates (-41.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	68	10	78

Merged error: 6.0b

Counts

78 → 10

regimes551.0ms

Accuracy

96.2% (0.9b remaining)

Error of 6.1b against oracle of 5.2b and baseline of 29.4b

bsearch100.0ms

Steps

Iters	Range	Point
8	6.202982415587433e+102	2.7805631612024945e+105	9.027388520595384e+104
11	2.479370203372984e-285	1.1635308969669537e-265	2.5062143377504272e-285
8	-3.8369784623857795e+111	-1.1680465845051113e+107	-1.4109566075029235e+110

Iters

Range

Point

6.202982415587433e+102

2.7805631612024945e+105

9.027388520595384e+104

2.479370203372984e-285

1.1635308969669537e-265

2.5062143377504272e-285

-3.8369784623857795e+111

-1.1680465845051113e+107

-1.4109566075029235e+110

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	127	63
1	127	63

end0.0ms

sample1.3s

Algorithm

intervals

Results

347.0ms	1104×	body	2560	valid
276.0ms	5070×	body	80	valid
239.0ms	934×	body	1280	valid
93.0ms	456×	body	640	valid
51.0ms	130×	body	5120	valid
37.0ms	690×	body	80	nan
33.0ms	211×	body	320	valid
21.0ms	357×	body	80	invalid
10.0ms	95×	body	160	valid

Details

analyze469.0ms

sample44.0ms

simplify210.0ms

prune8.0ms

localize9.0ms

rewrite30.0ms

series71.0ms

simplify72.0ms

prune91.0ms

localize13.0ms

rewrite42.0ms

series144.0ms

simplify36.0ms

prune91.0ms

localize13.0ms

rewrite30.0ms

series96.0ms

simplify49.0ms

prune65.0ms

localize10.0ms

rewrite22.0ms

series45.0ms

simplify30.0ms

prune53.0ms

regimes551.0ms

bsearch100.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling