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

sample121.0ms

Algorithm

intervals

Results

34.0ms	47×	body	1280	invalid
27.0ms	237×	body	80	valid
19.0ms	31×	body	640	invalid
5.0ms	15×	body	320	invalid
5.0ms	6×	body	1280	valid
5.0ms	9×	body	640	valid
3.0ms	14×	body	160	invalid
1.0ms	11×	body	80	invalid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify511.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

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: 33.8b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.2b	(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)))

rewrite36.0ms

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)
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
9.0ms	(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)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (atan2.f64 x.im x.re) y.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)))
60.0ms	(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)))

simplify104.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4801	676
1	4801	676

prune98.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 20.0b

Counts

70 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.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)
1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-l_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-log-exp_binary64`
6×	`associate-r_binary64`
3×	`log-pow_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `exp-diff_binary64` `rem-sqrt-square_binary64` `exp-sum_binary64` `flip-+_binary64`

Counts

4 → 68

Calls

4 calls:

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

series79.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(exp.f64 (-.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)))
28.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
8.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
9.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5267	840

prune93.0ms

Filtered

61 candidates to 80 candidates (-31.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	78	7	85

Merged error: 4.6b

Counts

85 → 7

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`unpow-prod-down_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `sqr-pow_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `div-exp_binary64`
2×	`add-log-exp_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

2 → 63

Calls

2 calls:

6.0ms	(/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series42.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
8.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify43.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4924	928
1	4924	928

prune78.0ms

Filtered

46 candidates to 69 candidates (-50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	67	9	76

Merged error: 4.6b

Counts

76 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x.re)
0.6b	(cbrt.f64 x.re)
0.6b	(cbrt.f64 x.re)
1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r_binary64` `pow1/3_binary64` `associate-l_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 51

Calls

4 calls:

1.0ms	(cbrt.f64 x.re)
1.0ms	(cbrt.f64 x.re)
1.0ms	(cbrt.f64 x.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series95.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt.f64 x.re)
27.0ms	(cbrt.f64 x.re)
30.0ms	(cbrt.f64 x.re)
8.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify25.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5413	291

prune51.0ms

Filtered

49 candidates to 63 candidates (-28.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	63	9	72

Merged error: 4.6b

Counts

72 → 9

regimes434.0ms

Accuracy

59% (6.4b remaining)

Error of 10.3b against oracle of 3.8b and baseline of 19.5b

bsearch239.0ms

Steps

Iters	Range	Point
7	3.855574762716742e-36	1.1904091354241852e-34	7.691521858662134e-35
10	4.1136646491794746e-182	3.0420156237048115e-172	2.432862549184466e-179
9	-1.0382332020571772e-299	-9.460081165269269e-306	-9.571765797869584e-306

Iters

Range

Point

3.855574762716742e-36

1.1904091354241852e-34

7.691521858662134e-35

4.1136646491794746e-182

3.0420156237048115e-172

2.432862549184466e-179

-1.0382332020571772e-299

-9.460081165269269e-306

-9.571765797869584e-306

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	62
1	83	62

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	1934×	body	1280	invalid
833.0ms	7569×	body	80	valid
610.0ms	1261×	body	640	invalid
179.0ms	519×	body	320	invalid
95.0ms	129×	body	1280	valid
79.0ms	165×	body	640	valid
55.0ms	245×	body	160	invalid
47.0ms	404×	body	80	invalid
29.0ms	87×	body	320	valid
12.0ms	50×	body	160	valid

Details

analyze1.3s

sample121.0ms

simplify511.0ms

prune15.0ms

localize24.0ms

rewrite36.0ms

series82.0ms

simplify104.0ms

prune98.0ms

localize16.0ms

rewrite20.0ms

series79.0ms

simplify48.0ms

prune93.0ms

localize10.0ms

rewrite12.0ms

series42.0ms

simplify43.0ms

prune78.0ms

localize16.0ms

rewrite9.0ms

series95.0ms

simplify25.0ms

prune51.0ms

regimes434.0ms

bsearch239.0ms

simplify3.0ms

end0.0ms

sample3.7s

Profiling