Details

analyze261.0ms

Algorithm

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

sample30.0ms

Algorithm

intervals

Results

11.0ms	247×	body	128	valid
8.0ms	288×	pre	128	true
1.0ms	32×	body	128	nan
1.0ms	9×	body	256	valid

simplify273.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (267.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	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: 28.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
28.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite38.0ms

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:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

series533.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
223.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
132.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

simplify68.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5008	1963

prune83.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 0.4b

Counts

83 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.3b	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`associate-/l*_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
16.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

series879.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
132.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
310.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
371.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5155	3003

prune127.0ms

Filtered

76 candidates to 110 candidates (-44.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Merged error: 0.0b

Counts

115 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`pow1_binary64`
4×	`associate-/r*_binary64` `associate-/r/_binary64`
3×	`flip3-+_binary64` `associate-l_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

13.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
11.0ms	(/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

series771.0ms

Counts

4 → 12

Calls

4 calls:

379.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
67.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
204.0ms	(/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
121.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4903	2595
1	4903	2595

prune110.0ms

Filtered

77 candidates to 105 candidates (-36.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Merged error: 0b

Counts

113 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.3b	(/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
10.0ms	(/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))

series690.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
62.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
134.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
376.0ms	(/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4913	1662
1	4913	1662

prune63.0ms

Filtered

56 candidates to 75 candidates (-33.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	76	7	83

Merged error: 0b

Counts

83 → 7

regimes58.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	24
1	60	24

end0.0ms

sample844.0ms

Algorithm

intervals

Results

349.0ms	7690×	body	128	valid
240.0ms	8804×	pre	128	true
37.0ms	804×	body	128	nan
29.0ms	310×	body	256	valid

Details

analyze261.0ms

sample30.0ms

simplify273.0ms

prune4.0ms

localize11.0ms

rewrite38.0ms

series533.0ms

simplify68.0ms

prune83.0ms

localize14.0ms

rewrite51.0ms

series879.0ms

simplify60.0ms

prune127.0ms

localize10.0ms

rewrite44.0ms

series771.0ms

simplify90.0ms

prune110.0ms

localize11.0ms

rewrite31.0ms

series690.0ms

simplify72.0ms

prune63.0ms

regimes58.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample844.0ms

Profiling