Details

analyze1.5s

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

sample136.0ms

Algorithm

intervals

Results

49.0ms	66×	body	1280	invalid
30.0ms	234×	body	80	valid
15.0ms	30×	body	640	invalid
8.0ms	23×	body	320	invalid
5.0ms	10×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	6×	body	160	valid
1.0ms	6×	body	160	invalid
1.0ms	9×	body	80	invalid
1.0ms	3×	body	320	valid

simplify482.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune22.0ms

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: 32.6b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.6b	(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.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)))
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)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

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)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
65.0ms	(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)))

simplify73.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4920	677
1	4920	677

prune100.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	6	69

Merged error: 18.9b

Counts

69 → 6

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))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.5b	(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)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(-.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)))

simplify56.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4914	886
1	4914	886

prune92.0ms

Filtered

57 candidates to 77 candidates (-35.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 5.0b

Counts

83 → 7

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`pow1_binary64` `associate-l_binary64`
6×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`log-pow_binary64`

Counts

2 → 37

Calls

2 calls:

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

series15.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify42.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5009	267

prune50.0ms

Filtered

26 candidates to 43 candidates (-65.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	43	7	50

Merged error: 5.0b

Counts

50 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.6b	(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.im)
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)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

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)))
6.0ms	(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)))

simplify73.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4920	677
1	4920	677

prune64.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	68	7	75

Merged error: 5.0b

Counts

75 → 7

regimes400.0ms

Accuracy

83.2% (5.4b remaining)

Error of 9.0b against oracle of 3.6b and baseline of 35.8b

bsearch75.0ms

Steps

Iters	Range		Point
8	-1.8895882811869054e-305	5.648564199708531e-308	4.90816831678503e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	27
1	59	27

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	1817×	body	1280	invalid
839.0ms	7543×	body	80	valid
586.0ms	1199×	body	640	invalid
191.0ms	548×	body	320	invalid
89.0ms	175×	body	640	valid
84.0ms	118×	body	1280	valid
52.0ms	415×	body	80	invalid
52.0ms	230×	body	160	invalid
34.0ms	94×	body	320	valid
16.0ms	70×	body	160	valid

Details

analyze1.5s

sample136.0ms

simplify482.0ms

prune22.0ms

localize24.0ms

rewrite25.0ms

series85.0ms

simplify73.0ms

prune100.0ms

localize17.0ms

rewrite21.0ms

series68.0ms

simplify56.0ms

prune92.0ms

localize11.0ms

rewrite12.0ms

series15.0ms

simplify42.0ms

prune50.0ms

localize26.0ms

rewrite22.0ms

series68.0ms

simplify73.0ms

prune64.0ms

regimes400.0ms

bsearch75.0ms

simplify2.0ms

end0.0ms

sample3.6s

Profiling