Details

sample12.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.125122%

Guaranteed chance to sample good point: 55.092126%

Results

48.0ms	63×	body	1280	invalid
31.0ms	238×	body	80	valid
26.0ms	52×	body	640	invalid
6.0ms	18×	body	320	invalid
4.0ms	5×	body	1280	valid
3.0ms	7×	body	320	valid
2.0ms	4×	body	640	valid
2.0ms	8×	body	160	invalid
2.0ms	1×	body	2560	invalid
2.0ms	14×	body	80	invalid
1.0ms	2×	body	160	valid

simplify407.0ms

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

prune15.0ms

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: 31.9b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.im)
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

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)
17.0ms	(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)))

series85.0ms

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)))
66.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify85.0ms

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

prune148.0ms

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	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	8	69

Merged error: 16.5b

Counts

69 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.1b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
24.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify69.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (61.0ms)

Iter	Nodes	Cost
0	158	616
1	336	558
2	704	557
3	2021	557
4	5001	554

prune141.0ms

Filtered

56 candidates to 65 candidates (-16.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	65	8	73

Merged error: 16.5b

Counts

73 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

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)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify63.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (56.0ms)

Iter	Nodes	Cost
0	152	580
1	321	508
2	672	505
3	1724	505
4	5001	504

prune119.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	51	8	59

Merged error: 16.5b

Counts

59 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

12.3b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.1b	(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)))

series123.0ms

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)))
56.0ms	(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 (13.0ms)

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

prune107.0ms

Filtered

55 candidates to 71 candidates (-29.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	70	9	79

Merged error: 16.5b

Counts

79 → 9

regimes485.0ms

Accuracy

78.3% (3.1b remaining)

Error of 22.3b against oracle of 19.2b and baseline of 33.5b

bsearch156.0ms

Steps

Iters	Range		Point
11	-1.9588819608475904e-288	1.3548092070447711e-307	-3.78534904918826e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35

end0.0ms

sample16.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.125122%

Guaranteed chance to sample good point: 55.092126%

Results

1.6s	2137×	body	1280	invalid
846.0ms	7509×	body	80	valid
634.0ms	1299×	body	640	invalid
163.0ms	467×	body	320	invalid
91.0ms	130×	body	1280	valid
86.0ms	179×	body	640	valid
52.0ms	31×	body	2560	invalid
51.0ms	217×	body	160	invalid
45.0ms	391×	body	80	invalid
40.0ms	118×	body	320	valid
15.0ms	64×	body	160	valid

Details

sample12.6s

simplify407.0ms

prune15.0ms

localize26.0ms

rewrite35.0ms

series85.0ms

simplify85.0ms

prune148.0ms

localize30.0ms

rewrite36.0ms

series74.0ms

simplify69.0ms

prune141.0ms

localize29.0ms

rewrite25.0ms

series174.0ms

simplify63.0ms

prune119.0ms

localize26.0ms

rewrite20.0ms

series123.0ms

simplify49.0ms

prune107.0ms

regimes485.0ms

bsearch156.0ms

simplify2.0ms

end0.0ms

sample16.8s

Profiling