Details

analyze802.0ms

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

sample37.0ms

Algorithm

intervals

Results

10.0ms	198×	body	80	valid
8.0ms	26×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	10×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

prune4.0ms

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: 12.0b

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)))))))
1.4b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
16.6b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite49.0ms

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))))
15.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
10.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
25.0ms	(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)))))
7.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify85.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5424	1453

prune102.0ms

Filtered

74 candidates to 93 candidates (-25.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	83	10	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Merged error: 11.7b

Counts

94 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
8.6b	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
16.6b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
16.6b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite50.0ms

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:

20.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
13.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x 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)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
13.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify95.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4952	1842
1	4952	1842

prune113.0ms

Filtered

84 candidates to 137 candidates (-63.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	135	12	147

Merged error: 11.7b

Counts

147 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

8.4b	(+.f64 1 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))))
16.6b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
16.6b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
16.6b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite46.0ms

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:

21.0ms	(+.f64 1 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))))
9.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
8.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series129.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+.f64 1 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))))
13.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
13.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
13.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4921	1333
1	4921	1333

prune116.0ms

Filtered

59 candidates to 69 candidates (-16.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	69	12	81

Merged error: 11.7b

Counts

81 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

8.4b	(+.f64 1 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))))))
16.6b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
16.6b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
16.6b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

rewrite32.0ms

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:

12.0ms	(+.f64 1 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+.f64 1 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))))))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4921	1333
1	4921	1333

prune114.0ms

Filtered

57 candidates to 69 candidates (-21.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	4	6	10
Picked	1	0	1
Done	1	0	1
Total	71	10	81

Merged error: 11.7b

Counts

81 → 10

regimes112.0ms

Accuracy

81.9% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 14.5b

bsearch27.0ms

Steps

Iters	Range		Point
9	-1.2747404973239997e-103	-1.2642247619625633e-111	-1.2651948696730856e-107

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	67
1	68	67

end0.0ms

sample1.1s

Algorithm

intervals

Results

314.0ms	6048×	body	80	valid
250.0ms	786×	body	2560	valid
160.0ms	604×	body	1280	valid
136.0ms	8000×	pre	80	true
66.0ms	321×	body	640	valid
25.0ms	164×	body	320	valid
8.0ms	77×	body	160	valid

Details

analyze802.0ms

sample37.0ms

simplify6.0ms

prune4.0ms

localize11.0ms

rewrite49.0ms

series56.0ms

simplify85.0ms

prune102.0ms

localize14.0ms

rewrite50.0ms

series36.0ms

simplify95.0ms

prune113.0ms

localize23.0ms

rewrite46.0ms

series129.0ms

simplify52.0ms

prune116.0ms

localize23.0ms

rewrite32.0ms

series90.0ms

simplify53.0ms

prune114.0ms

regimes112.0ms

bsearch27.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling