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
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

sample148.0ms

Algorithm

intervals

Results

55.0ms	74×	body	1280	invalid
32.0ms	245×	body	80	valid
23.0ms	44×	body	640	invalid
8.0ms	19×	body	320	invalid
3.0ms	2×	body	2560	invalid
2.0ms	15×	body	80	invalid
2.0ms	3×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	5×	body	160	invalid
1.0ms	4×	body	160	valid
1.0ms	2×	body	320	valid

simplify647.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4950	72
1	4950	72

prune8.0ms

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: 32.3b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.5b	(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)))

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` `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.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)))
23.0ms	(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)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
23.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
24.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
225.0ms	(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)))

simplify128.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4838	1270
1	4838	1270

prune117.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 18.2b

Counts

69 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

3.1b	(cbrt.f64 (atan2.f64 x.im x.re))
28.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.5b	(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)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`*-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×	`cbrt-prod_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow1/3_binary64` `sin-sum_binary64`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
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)))
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)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
26.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
26.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
198.0ms	(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)))

simplify80.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5029	1162

prune98.0ms

Filtered

53 candidates to 61 candidates (-15.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	60	8	68

Merged error: 18.2b

Counts

68 → 8

localize39.0ms

Local error

Found 4 expressions with local error:

28.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.5b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
33.5b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
33.5b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`sin-sum_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 39

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
8.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

series597.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
192.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
192.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
189.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

simplify88.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5044	1579

prune175.0ms

Filtered

49 candidates to 51 candidates (-4.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	51	8	59

Merged error: 18.2b

Counts

59 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (atan2.f64 x.im x.re) y.re)
0.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
16.6b	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
28.8b	(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`
9×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sin-sum_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 59

Calls

4 calls:

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

series225.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
27.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
147.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
26.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify131.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4839	1147
1	4839	1147

prune69.0ms

Filtered

54 candidates to 71 candidates (-31.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	69	10	79

Merged error: 12.4b

Counts

79 → 10

regimes275.0ms

Accuracy

74.5% (5.3b remaining)

Error of 18.4b against oracle of 13.1b and baseline of 33.8b

bsearch124.0ms

Steps

Iters	Range		Point
9	-3.012847183078543e-303	2.7494504005465715e-308	2.7935567998281e-310

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	80	117
1	80	117

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	2104×	body	1280	invalid
855.0ms	7557×	body	80	valid
664.0ms	1323×	body	640	invalid
170.0ms	481×	body	320	invalid
101.0ms	132×	body	1280	valid
75.0ms	155×	body	640	valid
65.0ms	39×	body	2560	invalid
45.0ms	386×	body	80	invalid
40.0ms	174×	body	160	invalid
30.0ms	87×	body	320	valid
16.0ms	69×	body	160	valid

Details

analyze1.5s

sample148.0ms

simplify647.0ms

prune8.0ms

localize24.0ms

rewrite38.0ms

series297.0ms

simplify128.0ms

prune117.0ms

localize29.0ms

rewrite17.0ms

series301.0ms

simplify80.0ms

prune98.0ms

localize39.0ms

rewrite27.0ms

series597.0ms

simplify88.0ms

prune175.0ms

localize23.0ms

rewrite20.0ms

series225.0ms

simplify131.0ms

prune69.0ms

regimes275.0ms

bsearch124.0ms

simplify5.0ms

end0.0ms

sample4.0s

Profiling