Details

sample422.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.609375%

Results

59.0ms	77×	body	1280	valid
34.0ms	256×	body	80	valid
23.0ms	47×	body	640	valid
6.0ms	17×	body	320	valid
3.0ms	2×	body	2560	valid
1.0ms	4×	body	160	valid

simplify427.0ms

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

prune19.0ms

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

localize43.0ms

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)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

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

prune141.0ms

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)))

rewrite17.0ms

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

series76.0ms

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

simplify72.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (64.0ms)

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

localize31.0ms

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)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(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)))

simplify72.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (66.0ms)

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

prune121.0ms

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)))

rewrite22.0ms

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))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(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:

57.0ms	(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)))
53.0ms	(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

prune106.0ms

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

regimes463.0ms

Accuracy

77.7% (3.1b remaining)

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

bsearch113.0ms

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

1.7s	2233×	body	1280	valid
932.0ms	7996×	body	80	valid
699.0ms	1375×	body	640	valid
211.0ms	585×	body	320	valid
69.0ms	40×	body	2560	valid
54.0ms	232×	body	160	valid

Details

sample422.0ms

simplify427.0ms

prune19.0ms

localize43.0ms

rewrite21.0ms

series88.0ms

simplify80.0ms

prune141.0ms

localize26.0ms

rewrite17.0ms

series76.0ms

simplify72.0ms

prune124.0ms

localize31.0ms

rewrite15.0ms

series77.0ms

simplify72.0ms

prune121.0ms

localize25.0ms

rewrite22.0ms

series122.0ms

simplify49.0ms

prune106.0ms

regimes463.0ms

bsearch113.0ms

simplify2.0ms

end0.0ms

sample4.3s

Profiling