Details

analyze458.0ms

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

10.0ms	32×	body	2560	valid
8.0ms	160×	body	80	valid
8.0ms	32×	body	1280	valid
3.0ms	17×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	15×	body	80	nan
0.0ms	7×	body	80	invalid
0.0ms	3×	body	160	valid

simplify268.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (266.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune7.0ms

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: 34.5b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))) b) (.f64 3.0 a))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite216.0ms

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:

198.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))) b) (.f64 3.0 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))) b) (.f64 3.0 a))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))) b)
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4931	1311
1	4931	1311

prune128.0ms

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: 4.6b

Counts

83 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
3.3b	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))))) (.f64 3.0 a))
9.5b	(/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac_binary64`
77×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
19×	`distribute-lft-out_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
4×	`div-inv_binary64`
3×	`flip3-+_binary64` `div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `clear-num_binary64` `prod-exp_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 → 158

Calls

4 calls:

4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
14.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))))) (.f64 3.0 a))
10.0ms	(/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
54.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))))) (.f64 3.0 a))
88.0ms	(/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4961	3865
1	4961	3865

prune228.0ms

Filtered

126 candidates to 170 candidates (-34.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	168	2	170
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	170	10	180

Merged error: 4.6b

Counts

180 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3.0 a) c)
0.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite23.0ms

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:

6.0ms	(.f64 (.f64 3.0 a) c)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(.f64 (.f64 3.0 a) c)
18.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

simplify32.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5122	753

prune78.0ms

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: 4.6b

Counts

78 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 3.0 (.f64 a c))
0.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3.0 (*.f64 a c)))))
1.2b	(-.f64 (.f64 b b) (.f64 3.0 (*.f64 a c)))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3.0 (*.f64 a c))))

rewrite24.0ms

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-l_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-r_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

7.0ms	(.f64 3.0 (.f64 a c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3.0 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 3.0 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3.0 (*.f64 a c))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 3.0 (.f64 a c))
18.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3.0 (*.f64 a c)))))
10.0ms	(-.f64 (.f64 b b) (.f64 3.0 (*.f64 a c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3.0 (*.f64 a c))))

simplify48.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4953	752
1	4953	752

prune54.0ms

Filtered

47 candidates to 68 candidates (-44.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	68	10	78

Merged error: 4.6b

Counts

78 → 10

regimes327.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.3b against oracle of 5.3b and baseline of 30.0b

bsearch98.0ms

Steps

Iters	Range	Point
8	1.20489196718021e+121	2.0599351254817446e+124	2.3119185569929864e+122
10	-3.3146832752641835e-294	-2.1880019819224353e-304	-3.0932591459060287e-302
11	-1.3592398439034167e+155	-2.591577042876611e+131	-5.05350087668616e+142

Iters

Range

Point

1.20489196718021e+121

2.0599351254817446e+124

2.3119185569929864e+122

-3.3146832752641835e-294

-2.1880019819224353e-304

-3.0932591459060287e-302

-1.3592398439034167e+155

-2.591577042876611e+131

-5.05350087668616e+142

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	148	59
1	148	59

end0.0ms

sample1.3s

Algorithm

intervals

Results

339.0ms	1127×	body	2560	valid
264.0ms	5052×	body	80	valid
215.0ms	878×	body	1280	valid
93.0ms	478×	body	640	valid
40.0ms	106×	body	5120	valid
35.0ms	247×	body	320	valid
31.0ms	635×	body	80	nan
21.0ms	383×	body	80	invalid
11.0ms	112×	body	160	valid

Details

analyze458.0ms

sample43.0ms

simplify268.0ms

prune7.0ms

localize9.0ms

rewrite216.0ms

series77.0ms

simplify39.0ms

prune128.0ms

localize11.0ms

rewrite40.0ms

series169.0ms

simplify61.0ms

prune228.0ms

localize10.0ms

rewrite23.0ms

series54.0ms

simplify32.0ms

prune78.0ms

localize10.0ms

rewrite24.0ms

series50.0ms

simplify48.0ms

prune54.0ms

regimes327.0ms

bsearch98.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling