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
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

sample150.0ms

Algorithm

intervals

Results

52.0ms	73×	body	1280	invalid
29.0ms	49×	body	640	invalid
28.0ms	239×	body	80	valid
7.0ms	19×	body	320	invalid
4.0ms	5×	body	1280	valid
3.0ms	7×	body	640	valid
2.0ms	9×	body	160	invalid
1.0ms	3×	body	320	valid
1.0ms	7×	body	80	invalid
0.0ms	2×	body	160	valid

simplify530.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune14.0ms

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: 36.8b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
31.4b	(cos.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)))
32.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite38.0ms

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` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
7.0ms	(cos.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)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
62.0ms	(cos.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)))
8.0ms	(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)))

simplify77.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4920	677
1	4920	677

prune94.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 24.2b

Counts

69 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.2b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
1.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
32.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
3×	`log-pow_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 65

Calls

4 calls:

5.0ms	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
24.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
11.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4914	886
1	4914	886

prune92.0ms

Filtered

57 candidates to 77 candidates (-35.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	75	6	81

Merged error: 4.0b

Counts

81 → 6

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (log.f64 x.im) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.1b	(*.f64 (log.f64 x.im) y.re)
1.0b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64`
7×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l*_binary64`
6×	`associate-r_binary64`
5×	`add-log-exp_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `log-pow_binary64` `flip--_binary64`

Counts

3 → 48

Calls

3 calls:

4.0ms	(-.f64 (.f64 (log.f64 x.im) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
4.0ms	(*.f64 (log.f64 x.im) y.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series44.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(-.f64 (.f64 (log.f64 x.im) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
11.0ms	(*.f64 (log.f64 x.im) y.re)
9.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify58.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4986	450
1	4986	450

prune61.0ms

Filtered

36 candidates to 57 candidates (-58.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	57	6	63

Merged error: 4.0b

Counts

63 → 6

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.1b	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
1.0b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64`
7×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l*_binary64`
6×	`associate-r_binary64`
5×	`add-log-exp_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `log-pow_binary64` `flip--_binary64`

Counts

3 → 48

Calls

3 calls:

4.0ms	(-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
4.0ms	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series45.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
11.0ms	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
9.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify51.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5288	492

prune40.0ms

Filtered

36 candidates to 57 candidates (-58.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	57	6	63

Merged error: 4.0b

Counts

63 → 6

regimes425.0ms

Accuracy

83.3% (5.5b remaining)

Error of 9.0b against oracle of 3.6b and baseline of 36.3b

bsearch108.0ms

Steps

Iters	Range		Point
11	-2.742474779525847e-286	2.77114183577462e-295	-3.89342332684725e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	27
1	59	27

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	1948×	body	1280	invalid
845.0ms	7549×	body	80	valid
650.0ms	1314×	body	640	invalid
189.0ms	549×	body	320	invalid
100.0ms	138×	body	1280	valid
79.0ms	160×	body	640	valid
52.0ms	228×	body	160	invalid
46.0ms	396×	body	80	invalid
33.0ms	94×	body	320	valid
14.0ms	59×	body	160	valid

Details

analyze1.3s

sample150.0ms

simplify530.0ms

prune14.0ms

localize26.0ms

rewrite38.0ms

series95.0ms

simplify77.0ms

prune94.0ms

localize17.0ms

rewrite21.0ms

series84.0ms

simplify57.0ms

prune92.0ms

localize12.0ms

rewrite14.0ms

series44.0ms

simplify58.0ms

prune61.0ms

localize12.0ms

rewrite14.0ms

series45.0ms

simplify51.0ms

prune40.0ms

regimes425.0ms

bsearch108.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling