Details

analyze484.0ms

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
8.0ms	33×	body	1280	valid
2.0ms	5×	body	5120	valid
1.0ms	8×	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

simplify218.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (215.0ms)

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: 35.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 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 4 (.f64 a c)))) b) (.f64 a 2))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5261	1302

prune105.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 7.0b

Counts

83 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
0.8b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
1.2b	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
24.6b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

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`
3×	`distribute-lft-out--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_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` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
9.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
16.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
16.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

simplify70.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4910	1289
1	4910	1289

prune67.0ms

Filtered

59 candidates to 82 candidates (-39.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	83	9	92

Merged error: 6.9b

Counts

92 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 58

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4973	1008
1	4973	1008

prune73.0ms

Filtered

56 candidates to 70 candidates (-25.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	69	10	79

Merged error: 6.9b

Counts

79 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

10.0b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
25.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
25.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`cbrt-div_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`sqrt-prod_binary64`
2×	`pow1/3_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 52

Calls

4 calls:

13.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
24.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
24.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify37.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4992	1099
1	4992	1099

prune75.0ms

Filtered

58 candidates to 64 candidates (-10.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	64	10	74

Merged error: 6.9b

Counts

74 → 10

regimes272.0ms

Accuracy

84.5% (4.5b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 34.9b

bsearch43.0ms

Steps

Iters	Range		Point
8	5.135175781724241e-100	1.2604058359658631e-95	9.164205384495035e-97
6	-9.887771120288306e+104	-9.878666258180965e+103	-8.238967565051123e+104

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	35
1	58	35

end0.0ms

sample1.5s

Algorithm

intervals

Results

332.0ms	1113×	body	2560	valid
269.0ms	5067×	body	80	valid
239.0ms	688×	body	80	nan
221.0ms	906×	body	1280	valid
88.0ms	459×	body	640	valid
45.0ms	127×	body	5120	valid
32.0ms	225×	body	320	valid
18.0ms	357×	body	80	invalid
10.0ms	103×	body	160	valid

Details

analyze484.0ms

sample44.0ms

simplify218.0ms

prune6.0ms

localize10.0ms

rewrite31.0ms

series73.0ms

simplify43.0ms

prune105.0ms

localize10.0ms

rewrite33.0ms

series71.0ms

simplify70.0ms

prune67.0ms

localize13.0ms

rewrite31.0ms

series65.0ms

simplify46.0ms

prune73.0ms

localize21.0ms

rewrite29.0ms

series100.0ms

simplify37.0ms

prune75.0ms

regimes272.0ms

bsearch43.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling