Details

analyze317.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

sample30.0ms

Algorithm

intervals

Results

9.0ms	202×	body	80	valid
8.0ms	28×	body	2560	valid
3.0ms	9×	body	5120	valid
2.0ms	7×	body	1280	valid
1.0ms	7×	body	640	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	22	15
1	22	15

prune7.0ms

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: 37.5b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.5b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.6b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite26.0ms

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:

5.0ms	(+.f64 (.f64 re re) (.f64 im im))
8.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 (.f64 re re) (.f64 im im))
26.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4967	687
1	4967	687

prune65.0ms

Filtered

53 candidates to 63 candidates (-18.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	55	8	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	8	64

Merged error: 18.5b

Counts

64 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
5.3b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
29.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite47.0ms

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`
18×	`*-un-lft-identity_binary64` `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` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 124

Calls

4 calls:

17.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
16.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
8.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
9.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4944	1470
1	4944	1470

prune61.0ms

Filtered

72 candidates to 136 candidates (-88.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	136	8	144

Merged error: 18.5b

Counts

144 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
0.6b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
15.3b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))) 3))
29.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-prod_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `associate-*r/_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `flip-+_binary64`
3×	`sqrt-pow1_binary64`
2×	`cbrt-div_binary64` `pow1/2_binary64` `cube-div_binary64`
1×	`pow-prod-down_binary64` `rem-cbrt-cube_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `sqr-pow_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 65

Calls

4 calls:

8.0ms	(sqrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
6.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))) 3))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
7.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
26.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))) 3))
9.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify34.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5039	1075

prune59.0ms

Filtered

58 candidates to 77 candidates (-32.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	75	10	85

Merged error: 18.5b

Counts

85 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.9b	(cbrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
15.3b	(cbrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))) 3))
29.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-div_binary64`
16×	`associate-*r/_binary64`
10×	`sqrt-div_binary64`
9×	`flip3-+_binary64` `add-sqr-sqrt_binary64` `flip-+_binary64` `cbrt-prod_binary64`
8×	`cube-div_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-times_binary64`
2×	`pow1/2_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-*l/_binary64`
1×	`rem-cbrt-cube_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 66

Calls

4 calls:

8.0ms	(cbrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
5.0ms	(cbrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))) 3))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cbrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
61.0ms	(cbrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))) 3))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4950	1703
1	4950	1703

prune65.0ms

Filtered

67 candidates to 78 candidates (-16.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	78	10	88

Merged error: 18.5b

Counts

88 → 10

regimes256.0ms

Accuracy

55.5% (9.5b remaining)

Error of 26.8b against oracle of 17.3b and baseline of 38.7b

bsearch42.0ms

Steps

Iters	Range		Point
7	8.898429448585728e+53	2.403331621865471e+55	4.72639369204056e+54
9	7.888357124305722e-164	9.968732408803144e-155	1.540540874146605e-163
9	-7.733353912735179e-299	-1.087377105792989e-304	-2.05568490709924e-302

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	74
1	58	74

end0.0ms

sample903.0ms

Algorithm

intervals

Results

278.0ms	5993×	body	80	valid
195.0ms	708×	body	2560	valid
111.0ms	499×	body	1280	valid
103.0ms	299×	body	5120	valid
49.0ms	281×	body	640	valid
20.0ms	152×	body	320	valid
6.0ms	68×	body	160	valid

Details

analyze317.0ms

sample30.0ms

simplify5.0ms

prune7.0ms

localize10.0ms

rewrite26.0ms

series46.0ms

simplify63.0ms

prune65.0ms

localize12.0ms

rewrite47.0ms

series31.0ms

simplify67.0ms

prune61.0ms

localize12.0ms

rewrite24.0ms

series69.0ms

simplify34.0ms

prune59.0ms

localize19.0ms

rewrite24.0ms

series106.0ms

simplify54.0ms

prune65.0ms

regimes256.0ms

bsearch42.0ms

simplify3.0ms

end0.0ms

sample903.0ms

Profiling