Details

analyze360.0ms

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

sample36.0ms

Algorithm

intervals

Results

10.0ms	189×	body	80	valid
7.0ms	21×	body	2560	valid
5.0ms	21×	body	1280	valid
3.0ms	7×	body	5120	valid
2.0ms	9×	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	22	15
1	22	15

prune6.0ms

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: 41.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.0b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite27.0ms

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))
9.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+.f64 (.f64 re re) (.f64 im im))
30.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
11.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4967	687
1	4967	687

prune109.0ms

Filtered

53 candidates to 63 candidates (-18.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	54	9	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	9	64

Merged error: 21.3b

Counts

64 → 9

localize14.0ms

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)))))
7.0b	(+.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)
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

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`
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)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify69.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4944	1470
1	4944	1470

prune111.0ms

Filtered

71 candidates to 136 candidates (-91.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	136	9	145

Merged error: 21.3b

Counts

145 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
6.5b	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
31.2b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.2b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
9×	`associate-r_binary64`
8×	`sqrt-prod_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64`
2×	`associate-*r/_binary64` `pow1/3_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 65

Calls

4 calls:

9.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
10.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
32.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
22.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
25.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4945	1404
1	4945	1404

prune111.0ms

Filtered

68 candidates to 77 candidates (-13.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	76	10	86

Merged error: 21.3b

Counts

86 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

11.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `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×	`+-commutative_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

25.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5310	612

prune69.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	68	10	78

Merged error: 21.3b

Counts

78 → 10

regimes330.0ms

Accuracy

57.2% (9.4b remaining)

Error of 26.9b against oracle of 17.5b and baseline of 39.4b

bsearch47.0ms

Steps

Iters	Range		Point
0	1.6562206752772235e+136	1.6741129710535287e+136	1.665166823165376e+136
9	3.928784151661965e-254	3.1808294008083687e-249	3.98296718739982e-254
8	1.2597963522294294e-278	1.3174351383314836e-275	1.3032785344699448e-275
6	-3.1400830244957616e-298	-3.828280990086513e-299	-1.8219756175958796e-298

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	79
1	64	79

end0.0ms

sample1.0s

Algorithm

intervals

Results

324.0ms	6023×	body	80	valid
222.0ms	714×	body	2560	valid
118.0ms	301×	body	5120	valid
114.0ms	443×	body	1280	valid
60.0ms	286×	body	640	valid
26.0ms	155×	body	320	valid
8.0ms	78×	body	160	valid

Details

analyze360.0ms

sample36.0ms

simplify5.0ms

prune6.0ms

localize11.0ms

rewrite27.0ms

series56.0ms

simplify60.0ms

prune109.0ms

localize14.0ms

rewrite50.0ms

series32.0ms

simplify69.0ms

prune111.0ms

localize15.0ms

rewrite30.0ms

series118.0ms

simplify64.0ms

prune111.0ms

localize15.0ms

rewrite40.0ms

series32.0ms

simplify57.0ms

prune69.0ms

regimes330.0ms

bsearch47.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling