Details

analyze800.0ms

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

sample38.0ms

Algorithm

intervals

Results

9.0ms	190×	body	80	valid
8.0ms	27×	body	2560	valid
4.0ms	18×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	12×	body	640	valid
1.0ms	6×	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	38	17
1	38	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: 14.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x))
0.0b	(sqrt.f64 (.f64 0.5 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (.f64 x x)))))))
1.2b	(+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x)))))
13.3b	(sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

6.0ms	(+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x))
14.0ms	(sqrt.f64 (.f64 0.5 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (.f64 x x)))))))
17.0ms	(+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x))
41.0ms	(sqrt.f64 (.f64 0.5 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (.f64 x x)))))))
14.0ms	(+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x)))))
9.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5214	875

prune101.0ms

Filtered

55 candidates to 63 candidates (-14.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	53	10	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	10	64

Merged error: 14.1b

Counts

64 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))
8.2b	(+.f64 1.0 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod_binary64`
50×	`add-sqr-sqrt_binary64`
34×	`sqrt-pow1_binary64`
29×	`pow1_binary64`
28×	`sqrt-div_binary64`
20×	`*-un-lft-identity_binary64`
18×	`pow1/2_binary64` `add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `pow-prod-up_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`frac-times_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 125

Calls

4 calls:

19.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))
10.0ms	(+.f64 1.0 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))
15.0ms	(+.f64 1.0 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))))
9.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))
9.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5089	1899

prune160.0ms

Filtered

84 candidates to 137 candidates (-63.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	134	13	147

Merged error: 14.1b

Counts

147 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

8.5b	(+.f64 1.0 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x)))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x))))))))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

11.0ms	(+.f64 1.0 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x)))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x))))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+.f64 1.0 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x)))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x))))))))
11.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))
9.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))
9.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))

simplify61.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4938	1360
1	4938	1360

prune175.0ms

Filtered

59 candidates to 69 candidates (-16.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	68	14	82

Merged error: 14.1b

Counts

82 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

8.5b	(+.f64 1.0 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x)))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x))))))))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

14.0ms	(+.f64 1.0 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x)))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x))))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+.f64 1.0 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x)))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x))))))))
9.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))
9.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))
9.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4938	1360
1	4938	1360

prune136.0ms

Filtered

57 candidates to 69 candidates (-21.1%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	61	8	69
Fresh	5	7	12
Picked	0	1	1
Done	0	1	1
Total	66	17	83

Merged error: 14.1b

Counts

83 → 17

regimes182.0ms

Accuracy

0% (1.2b remaining)

Error of 14.3b against oracle of 13.0b and baseline of 14.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	30
1	21	30

end0.0ms

sample1.1s

Algorithm

intervals

Results

310.0ms	6030×	body	80	valid
253.0ms	795×	body	2560	valid
155.0ms	610×	body	1280	valid
140.0ms	8000×	pre	80	true
72.0ms	356×	body	640	valid
21.0ms	146×	body	320	valid
7.0ms	63×	body	160	valid

Details

analyze800.0ms

sample38.0ms

simplify5.0ms

prune5.0ms

localize10.0ms

rewrite44.0ms

series72.0ms

simplify46.0ms

prune101.0ms

localize13.0ms

rewrite48.0ms

series43.0ms

simplify39.0ms

prune160.0ms

localize22.0ms

rewrite30.0ms

series96.0ms

simplify61.0ms

prune175.0ms

localize19.0ms

rewrite34.0ms

series95.0ms

simplify48.0ms

prune136.0ms

regimes182.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling