Details

analyze784.0ms

Algorithm

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

sample40.0ms

Algorithm

intervals

Results

10.0ms	198×	body	80	valid
8.0ms	27×	body	2560	valid
4.0ms	256×	pre	80	true
4.0ms	16×	body	1280	valid
1.0ms	7×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 11.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
1.2b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
15.9b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
16×	`sqrt-prod_binary64`
8×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`sqrt-pow1_binary64` `associate-/l*_binary64`
2×	`pow1/2_binary64` `associate-*r/_binary64` `associate-/r/_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 81

Calls

4 calls:

9.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
14.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
30.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
17.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
9.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5424	1453

prune146.0ms

Filtered

74 candidates to 93 candidates (-25.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	11	94

Merged error: 11.6b

Counts

94 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
0.9b	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
1.2b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
15.9b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `pow1_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
5×	`log-pow_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64` `exp-prod_binary64`
3×	`flip3-+_binary64` `log-prod_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `associate-*r/_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

14.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
2.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
34.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
15.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
9.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify99.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4857	1014
1	4857	1014

prune123.0ms

Filtered

63 candidates to 68 candidates (-7.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	67	12	79

Merged error: 11.6b

Counts

79 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
7.1b	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
15.9b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
15.9b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod_binary64`
30×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
27×	`times-frac_binary64`
9×	`associate-/r*_binary64`
8×	`sqrt-div_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/l*_binary64`
2×	`pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 94

Calls

4 calls:

10.0ms	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
4.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
15.0ms	(+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
8.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
9.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4946	1751
1	4946	1751

prune175.0ms

Filtered

80 candidates to 106 candidates (-32.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	105	13	118

Merged error: 11.6b

Counts

118 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
7.5b	(+.f64 1 (/.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))
15.9b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
15.9b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

10.0ms	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
74.0ms	(+.f64 1 (/.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
15.0ms	(+.f64 1 (/.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))
11.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
8.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4932	1759
1	4932	1759

prune129.0ms

Filtered

80 candidates to 107 candidates (-33.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	107	13	120

Merged error: 11.6b

Counts

120 → 13

regimes139.0ms

Accuracy

0% (1.2b remaining)

Error of 13.5b against oracle of 12.3b and baseline of 13.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	32
1	24	32

end0.0ms

sample1.1s

Algorithm

intervals

Results

314.0ms	6125×	body	80	valid
247.0ms	792×	body	2560	valid
148.0ms	555×	body	1280	valid
142.0ms	8000×	pre	80	true
57.0ms	295×	body	640	valid
24.0ms	155×	body	320	valid
8.0ms	78×	body	160	valid

Details

analyze784.0ms

sample40.0ms

simplify5.0ms

prune5.0ms

localize11.0ms

rewrite44.0ms

series67.0ms

simplify82.0ms

prune146.0ms

localize16.0ms

rewrite37.0ms

series88.0ms

simplify99.0ms

prune123.0ms

localize14.0ms

rewrite29.0ms

series62.0ms

simplify43.0ms

prune175.0ms

localize17.0ms

rewrite99.0ms

series63.0ms

simplify55.0ms

prune129.0ms

regimes139.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling