Details

analyze459.0ms

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

sample35.0ms

Algorithm

intervals

Results

8.0ms	174×	body	128	valid
8.0ms	32×	body	2048	valid
4.0ms	24×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	9×	body	512	valid
1.0ms	12×	body	128	nan
1.0ms	6×	body	256	valid
0.0ms	10×	body	128	invalid

simplify261.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (254.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune4.0ms

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: 31.7b

Counts

2 → 1

localize13.0ms

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))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite35.0ms

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 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)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
80.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
125.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify83.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4911	1967
1	4911	1967

prune109.0ms

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: 5.3b

Counts

83 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.2b	(/.f64 (/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
9.8b	(/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite49.0ms

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:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
15.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
12.0ms	(/.f64 (.f64 (.f64 a 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)))

series914.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
278.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
391.0ms	(/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify77.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5005	3204

prune120.0ms

Filtered

78 candidates to 114 candidates (-46.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	115	9	124

Merged error: 5.2b

Counts

124 → 9

localize14.0ms

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)))))))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
3×	`pow-prod-down_binary64` `associate-l_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `div-exp_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 → 61

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

series640.0ms

Counts

4 → 12

Calls

4 calls:

342.0ms	(.f64 1/3 (.f64 1 (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
122.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify82.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4891	1511
1	4891	1511

prune71.0ms

Filtered

54 candidates to 73 candidates (-35.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	73	9	82

Merged error: 5.2b

Counts

82 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 3 a) c)
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite26.0ms

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

series329.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(.f64 (.f64 3 a) c)
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
119.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5002	1119

prune49.0ms

Filtered

48 candidates to 68 candidates (-41.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	68	9	77

Merged error: 5.2b

Counts

77 → 9

regimes182.0ms

Accuracy

95% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.5b

bsearch100.0ms

Steps

Iters	Range	Point
10	5.188585294020087e+125	1.1265301499675102e+136	1.1429453515296668e+130
8	-6.224161327461502e-252	-5.669378336441993e-256	-1.0972294854103117e-255
7	-1.5651851937325674e+88	-4.635952324960644e+86	-6.649876856688698e+87

Iters

Range

Point

5.188585294020087e+125

1.1265301499675102e+136

1.1429453515296668e+130

-6.224161327461502e-252

-5.669378336441993e-256

-1.0972294854103117e-255

-1.5651851937325674e+88

-4.635952324960644e+86

-6.649876856688698e+87

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	88
1	130	88

end0.0ms

sample1.1s

Algorithm

intervals

Results

272.0ms	1121×	body	2048	valid
257.0ms	5186×	body	128	valid
140.0ms	719×	body	1024	valid
106.0ms	362×	body	4096	valid
58.0ms	405×	body	512	valid
32.0ms	655×	body	128	nan
20.0ms	360×	body	128	invalid
19.0ms	207×	body	256	valid

Details

analyze459.0ms

sample35.0ms

simplify261.0ms

prune4.0ms

localize13.0ms

rewrite35.0ms

series538.0ms

simplify83.0ms

prune109.0ms

localize14.0ms

rewrite49.0ms

series914.0ms

simplify77.0ms

prune120.0ms

localize14.0ms

rewrite35.0ms

series640.0ms

simplify82.0ms

prune71.0ms

localize10.0ms

rewrite26.0ms

series329.0ms

simplify39.0ms

prune49.0ms

regimes182.0ms

bsearch100.0ms

simplify4.0ms

end0.0ms

sample1.1s

Profiling