Details

analyze1.3s

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
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

sample137.0ms

Algorithm

intervals

Results

57.0ms	72×	body	1280	invalid
28.0ms	244×	body	80	valid
16.0ms	33×	body	640	invalid
5.0ms	13×	body	320	invalid
3.0ms	4×	body	1280	valid
2.0ms	4×	body	640	valid
2.0ms	1×	body	2560	invalid
2.0ms	15×	body	80	invalid
1.0ms	5×	body	160	invalid
1.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify490.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 34.7b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(*.f64 (atan2.f64 x.im x.re) y.re)
29.8b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
66.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
17.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4957	686
1	4957	686

prune110.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 20.7b

Counts

70 → 8

localize31.0ms

Local error

Found 4 expressions with local error:

31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1/2_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4905	656
1	4905	656

prune105.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	71	9	80

Merged error: 20.7b

Counts

80 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1/2_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4905	656
1	4905	656

prune99.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	72	9	81

Merged error: 20.7b

Counts

81 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

12.4b	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re))) 3))
29.8b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`*-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` `sqrt-div_binary64`
3×	`unpow-prod-down_binary64` `cube-prod_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`rem-cbrt-cube_binary64` `pow1/3_binary64` `sin-sum_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 59

Calls

4 calls:

6.0ms	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re))) 3))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series128.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re))) 3))
56.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5332	1128

prune70.0ms

Filtered

55 candidates to 71 candidates (-29.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	70	10	80

Merged error: 20.7b

Counts

80 → 10

regimes392.0ms

Accuracy

72.7% (3.9b remaining)

Error of 22.9b against oracle of 18.9b and baseline of 33.3b

bsearch75.0ms

Steps

Iters	Range		Point
7	-5.432686138407363e-292	-1.6876537305142705e-293	-1.712157975876638e-293

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	65
1	70	65

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.5s	2104×	body	1280	invalid
844.0ms	7556×	body	80	valid
616.0ms	1242×	body	640	invalid
160.0ms	462×	body	320	invalid
92.0ms	129×	body	1280	valid
80.0ms	46×	body	2560	invalid
72.0ms	151×	body	640	valid
51.0ms	392×	body	80	invalid
36.0ms	162×	body	160	invalid
35.0ms	103×	body	320	valid
16.0ms	61×	body	160	valid

Details

analyze1.3s

sample137.0ms

simplify490.0ms

prune15.0ms

localize24.0ms

rewrite24.0ms

series99.0ms

simplify61.0ms

prune110.0ms

localize31.0ms

rewrite19.0ms

series29.0ms

simplify54.0ms

prune105.0ms

localize28.0ms

rewrite21.0ms

series29.0ms

simplify54.0ms

prune99.0ms

localize24.0ms

rewrite23.0ms

series128.0ms

simplify46.0ms

prune70.0ms

regimes392.0ms

bsearch75.0ms

simplify2.0ms

end0.0ms

sample4.0s

Profiling