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

sample113.0ms

Algorithm

intervals

Results

31.0ms	43×	body	1280	invalid
28.0ms	245×	body	80	valid
20.0ms	33×	body	640	invalid
5.0ms	14×	body	320	invalid
3.0ms	6×	body	640	valid
2.0ms	3×	body	1280	valid
2.0ms	10×	body	160	invalid
1.0ms	11×	body	80	invalid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify493.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune11.0ms

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: 34.0b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.8b	(*.f64 (atan2.f64 x.im x.re) y.re)
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.5b	(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)))

rewrite25.0ms

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.re)
5.0ms	(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)))
10.0ms	(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)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
6.0ms	(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)))
69.0ms	(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)))

simplify59.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4939	677
1	4939	677

prune67.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	7	69

Merged error: 18.4b

Counts

69 → 7

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)
1.2b	(*.f64 (atan2.f64 x.im x.re) y.im)
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite20.0ms

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:

4.0ms	(-.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)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(-.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))
20.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4914	886
1	4914	886

prune60.0ms

Filtered

57 candidates to 77 candidates (-35.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	74	10	84

Merged error: 2.4b

Counts

84 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

1.8b	(*.f64 (atan2.f64 x.im x.re) y.re)
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.5b	(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)))

rewrite22.0ms

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.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)))
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)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
10.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
48.0ms	(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)))

simplify58.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4939	677
1	4939	677

prune63.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	68	10	78

Merged error: 2.4b

Counts

78 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

1.8b	(*.f64 (atan2.f64 x.im x.re) y.re)
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.5b	(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)))

rewrite22.0ms

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.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)))
8.0ms	(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)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
6.0ms	(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)))
49.0ms	(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)))

simplify58.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4939	677
1	4939	677

prune48.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	68	10	78

Merged error: 2.4b

Counts

78 → 10

regimes378.0ms

Accuracy

69.9% (4.9b remaining)

Error of 8.4b against oracle of 3.5b and baseline of 19.8b

bsearch85.0ms

Steps

Iters	Range		Point
10	-6.535728959297307e-300	1.1300733600369329e-307	-3.2404748061479e-311

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	27
1	59	27

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	1947×	body	1280	invalid
835.0ms	7555×	body	80	valid
618.0ms	1286×	body	640	invalid
180.0ms	534×	body	320	invalid
89.0ms	122×	body	1280	valid
79.0ms	164×	body	640	valid
55.0ms	248×	body	160	invalid
48.0ms	423×	body	80	invalid
37.0ms	104×	body	320	valid
13.0ms	55×	body	160	valid

Details

analyze1.3s

sample113.0ms

simplify493.0ms

prune11.0ms

localize23.0ms

rewrite25.0ms

series90.0ms

simplify59.0ms

prune67.0ms

localize17.0ms

rewrite20.0ms

series67.0ms

simplify55.0ms

prune60.0ms

localize26.0ms

rewrite22.0ms

series71.0ms

simplify58.0ms

prune63.0ms

localize26.0ms

rewrite22.0ms

series69.0ms

simplify58.0ms

prune48.0ms

regimes378.0ms

bsearch85.0ms

simplify2.0ms

end0.0ms

sample3.7s

Profiling