Details

analyze480.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

sample25.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	90×	body	80	nan
1.0ms	26×	body	80	invalid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	8
1	14	8

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 18.8b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

1.6b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
6.0b	(/.f64 A (*.f64 V l))
13.6b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`times-frac_binary64`
6×	`pow1_binary64`
3×	`add-log-exp_binary64` `associate-l_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

3 → 66

Calls

3 calls:

8.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
4.0ms	(/.f64 A (*.f64 V l))
4.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

series37.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
6.0ms	(/.f64 A (*.f64 V l))
12.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

simplify71.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5085	561

prune117.0ms

Filtered

57 candidates to 75 candidates (-31.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	61	14	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	14	76

Merged error: 5.6b

Counts

76 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

1.6b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
2.1b	(/.f64 V (/.f64 (cbrt.f64 A) l))
3.1b	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
13.6b	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

849×	`times-frac_binary64`
358×	`add-sqr-sqrt_binary64`
331×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
157×	`sqrt-prod_binary64`
146×	`cbrt-prod_binary64`
93×	`associate-/r*_binary64`
79×	`associate-r_binary64`
32×	`add-exp-log_binary64`
24×	`div-inv_binary64`
23×	`add-cbrt-cube_binary64`
15×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`associate-/r/_binary64`
7×	`pow1_binary64`
6×	`unswap-sqr_binary64`
5×	`rem-sqrt-square_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64`
3×	`associate-l_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `-commutative_binary64`

Counts

4 → 463

Calls

4 calls:

30.0ms	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
7.0ms	(/.f64 V (/.f64 (cbrt.f64 A) l))
21.0ms	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
17.0ms	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
26.0ms	(/.f64 V (/.f64 (cbrt.f64 A) l))
11.0ms	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
16.0ms	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))

simplify101.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4973	7292
1	4973	7292

prune506.0ms

Filtered

417 candidates to 475 candidates (-13.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	462	13	475
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	468	21	489

Merged error: 1.8b

Counts

489 → 21

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
1.6b	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))))
1.7b	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
5.6b	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`times-frac_binary64` `cbrt-prod_binary64`
11×	`add-cbrt-cube_binary64`
10×	`pow1_binary64` `sqrt-prod_binary64`
6×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `associate-l_binary64`
2×	`cbrt-undiv_binary64` `associate-*r/_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r_binary64` `pow1/2_binary64` `associate-r_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt.f64 A)
10.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))))
8.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
5.0ms	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))

series133.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt.f64 A)
59.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))))
19.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
36.0ms	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))

simplify60.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4953	988
1	4953	988

prune149.0ms

Filtered

74 candidates to 90 candidates (-21.6%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	3	17	20
Picked	0	1	1
Done	0	0	0
Total	89	22	111

Merged error: 1.3b

Counts

111 → 22

localize17.0ms

Local error

Found 4 expressions with local error:

1.7b	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
1.7b	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
6.0b	(cbrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))
6.0b	(cbrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod_binary64`
24×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64`
12×	`associate-/l*_binary64`
8×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`cbrt-div_binary64` `associate-/r*_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`

Counts

4 → 92

Calls

4 calls:

6.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
6.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
5.0ms	(cbrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))
5.0ms	(cbrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
20.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
31.0ms	(cbrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))
34.0ms	(cbrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))

simplify57.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4932	946
1	4932	946

prune85.0ms

Filtered

82 candidates to 104 candidates (-26.8%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	20	20
Picked	0	1	1
Done	0	1	1
Total	104	22	126

Merged error: 1.3b

Counts

126 → 22

regimes1.0s

Accuracy

-7.1% (4.8b remaining)

Error of 6.4b against oracle of 1.6b and baseline of 6.1b

bsearch47.0ms

Steps

Iters	Range		Point
9	7.740698859183003e+215	6.150527533442182e+220	8.068698780946028e+215
5	2.460894195652485e+142	5.653024837172955e+142	5.565384703489568e+142

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	59
1	42	59

end0.0ms

sample702.0ms

Algorithm

intervals

Results

291.0ms	8000×	body	80	valid
96.0ms	2835×	body	80	nan
31.0ms	895×	body	80	invalid

Details

analyze480.0ms

sample25.0ms

simplify5.0ms

prune3.0ms

localize7.0ms

rewrite18.0ms

series37.0ms

simplify71.0ms

prune117.0ms

localize10.0ms

rewrite113.0ms

series76.0ms

simplify101.0ms

prune506.0ms

localize13.0ms

rewrite26.0ms

series133.0ms

simplify60.0ms

prune149.0ms

localize17.0ms

rewrite24.0ms

series104.0ms

simplify57.0ms

prune85.0ms

regimes1.0s

bsearch47.0ms

simplify2.0ms

end0.0ms

sample702.0ms

Profiling