Details

sample418.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.609375%

Results

60.0ms	73×	body	1280	invalid
29.0ms	241×	body	80	valid
20.0ms	41×	body	640	invalid
5.0ms	13×	body	320	invalid
3.0ms	2×	body	2560	invalid
3.0ms	6×	body	640	valid
3.0ms	4×	body	1280	valid
2.0ms	15×	body	80	invalid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	invalid
0.0ms	1×	body	160	valid

simplify426.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune20.0ms

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: 30.1b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.im)
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
73.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	206	434
1	539	395
2	1201	392
3	2732	392
4	5002	392

prune143.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 17.9b

Counts

70 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

4.9b	(cbrt (atan2 x.im x.re))
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow1/3`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(cbrt (atan2 x.im x.re))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify70.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (65.0ms)

Iter	Nodes	Cost
0	170	414
1	367	380
2	792	377
3	2193	377
4	5002	375

prune124.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	61	8	69

Merged error: 17.9b

Counts

69 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

4.9b	(cbrt (atan2 x.im x.re))
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow1/3`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(cbrt (atan2 x.im x.re))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify70.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (65.0ms)

Iter	Nodes	Cost
0	170	414
1	367	380
2	792	377
3	2193	377
4	5002	375

prune123.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	61	8	69

Merged error: 17.9b

Counts

69 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

9.3b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `cube-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cube-mult` `sin-sum` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

5.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify49.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	201	743
1	526	731
2	1327	729
3	5001	729

prune108.0ms

Filtered

54 candidates to 71 candidates (-31.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	69	10	79

Merged error: 17.9b

Counts

79 → 10

regimes491.0ms

Accuracy

77.7% (3.1b remaining)

Error of 22.5b against oracle of 19.4b and baseline of 33.4b

bsearch112.0ms

Steps

Iters	Range		Point
10	-1.2549265421453574e-303	4.6089327108154e-303	3.56287132922904e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	51
1	54	51

end0.0ms

sample4.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.609375%

Results

1.6s	2105×	body	1280	invalid
887.0ms	7571×	body	80	valid
633.0ms	1231×	body	640	invalid
167.0ms	474×	body	320	invalid
96.0ms	128×	body	1280	valid
72.0ms	144×	body	640	valid
68.0ms	40×	body	2560	invalid
51.0ms	425×	body	80	invalid
45.0ms	186×	body	160	invalid
40.0ms	111×	body	320	valid
11.0ms	46×	body	160	valid

Details

sample418.0ms

simplify426.0ms

prune20.0ms

localize24.0ms

rewrite21.0ms

series91.0ms

simplify81.0ms

prune143.0ms

localize26.0ms

rewrite15.0ms

series79.0ms

simplify70.0ms

prune124.0ms

localize33.0ms

rewrite16.0ms

series77.0ms

simplify70.0ms

prune123.0ms

localize25.0ms

rewrite20.0ms

series122.0ms

simplify49.0ms

prune108.0ms

regimes491.0ms

bsearch112.0ms

simplify2.0ms

end0.0ms

sample4.3s

Profiling