Details

analyze502.0ms

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

9.0ms	169×	body	80	valid
8.0ms	25×	body	2560	valid
7.0ms	28×	body	1280	valid
5.0ms	26×	body	640	valid
2.0ms	36×	body	80	nan
1.0ms	17×	body	80	invalid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify211.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (208.0ms)

Iter	Nodes	Cost
0	1801	16
1	1801	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: 35.1b

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))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite33.0ms

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:

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

series70.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify76.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4895	1297
1	4895	1297

prune98.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Merged error: 6.2b

Counts

83 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
2.2b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
10.8b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite39.0ms

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:

4.0ms	(-.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))
12.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.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)))

series144.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
50.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
69.0ms	(/.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)))

simplify39.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5324	2082

prune90.0ms

Filtered

75 candidates to 113 candidates (-50.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	114	9	123

Merged error: 6.1b

Counts

123 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c)))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
1.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64` `div-exp_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
5×	`associate-/r/_binary64`
4×	`cbrt-undiv_binary64`
3×	`flip3-+_binary64` `1-exp_binary64` `rec-exp_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `flip--_binary64` `pow-flip_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 75

Calls

4 calls:

12.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c)))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c)))
16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4958	1217
1	4958	1217

prune64.0ms

Filtered

59 candidates to 87 candidates (-47.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	87	9	96

Merged error: 6.1b

Counts

96 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.3b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
16.7b	(+.f64 b (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`log-prod_binary64` `exp-sum_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `log-pow_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `exp-diff_binary64` `log-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 60

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
7.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
9.0ms	(+.f64 b (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
17.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
23.0ms	(+.f64 b (exp.f64 (log.f64 (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

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5101	936

prune48.0ms

Filtered

54 candidates to 72 candidates (-33.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	71	10	81

Merged error: 6.1b

Counts

81 → 10

regimes393.0ms

Accuracy

94.6% (1.3b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 30.0b

bsearch90.0ms

Steps

Iters	Range	Point
6	2.854359690868473e+105	3.141868163273791e+106	2.9927405752514035e+106
10	-7.188044641578526e-301	1.6552434848760426e-306	-2.6232763968795353e-303
9	-2.3635877339385416e+100	-2.247531467469789e+94	-6.881450868076512e+99

Iters

Range

Point

2.854359690868473e+105

3.141868163273791e+106

2.9927405752514035e+106

-7.188044641578526e-301

1.6552434848760426e-306

-2.6232763968795353e-303

-2.3635877339385416e+100

-2.247531467469789e+94

-6.881450868076512e+99

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	116	62
1	116	62

end0.0ms

sample1.3s

Algorithm

intervals

Results

369.0ms	1116×	body	2560	valid
281.0ms	5078×	body	80	valid
243.0ms	923×	body	1280	valid
94.0ms	454×	body	640	valid
39.0ms	236×	body	320	valid
39.0ms	707×	body	80	nan
33.0ms	85×	body	5120	valid
22.0ms	359×	body	80	invalid
11.0ms	108×	body	160	valid

Details

analyze502.0ms

sample43.0ms

simplify211.0ms

prune6.0ms

localize10.0ms

rewrite33.0ms

series70.0ms

simplify76.0ms

prune98.0ms

localize13.0ms

rewrite39.0ms

series144.0ms

simplify39.0ms

prune90.0ms

localize12.0ms

rewrite30.0ms

series82.0ms

simplify60.0ms

prune64.0ms

localize16.0ms

rewrite27.0ms

series66.0ms

simplify49.0ms

prune48.0ms

regimes393.0ms

bsearch90.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling