Details

sample4.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.439453%

Guaranteed chance to sample good point: 55.118931%

Results

33.0ms	245×	body	80	valid
32.0ms	46×	body	1280	invalid
21.0ms	44×	body	640	invalid
5.0ms	16×	body	320	invalid
5.0ms	6×	body	1280	valid
2.0ms	10×	body	160	invalid
2.0ms	13×	body	80	invalid
1.0ms	2×	body	320	valid
0.0ms	1×	body	640	valid
0.0ms	2×	body	160	valid

simplify395.0ms

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: 33.8b

Counts

2 → 2

localize43.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (atan2 x.im x.re) y.im)
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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×	`cos-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)))
10.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (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)))
80.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify83.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	199	426
1	523	389
2	1179	387
3	2665	387
4	5002	387

prune125.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 20.8b

Counts

70 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.1b	(* (atan2 x.im x.re) y.im)
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
3×	`sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
24.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify81.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	307	551
1	925	510
2	2748	491
3	5002	491

prune125.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	75	9	84

Merged error: 2.9b

Counts

84 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (atan2 x.im x.re) y.im)
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

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×	`cos-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)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series75.0ms

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)))
57.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify82.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	199	426
1	523	389
2	1179	387
3	2665	387
4	5002	387

prune145.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	68	9	77

Merged error: 2.9b

Counts

77 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (atan2 x.im x.re) y.im)
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

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×	`cos-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)))
7.0ms	(cos (+ (* (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:

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)))
57.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify84.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	199	426
1	523	389
2	1179	387
3	2665	387
4	5002	387

prune95.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	68	9	77

Merged error: 2.9b

Counts

77 → 9

regimes434.0ms

Accuracy

65.8% (5.5b remaining)

Error of 9.3b against oracle of 3.9b and baseline of 19.8b

bsearch283.0ms

Steps

Iters	Range	Point
10	-3.2439133452398597e-305	6.515099016538699e-299	3.2994388420259e-310
6	-3.958580856072586e-192	-6.774811945833791e-193	-1.451418121449186e-192
8	-2.5085439748189628e-58	-1.434935671644135e-62	-2.8036328029487993e-59

Iters

Range

Point

-3.2439133452398597e-305

6.515099016538699e-299

3.2994388420259e-310

-3.958580856072586e-192

-6.774811945833791e-193

-1.451418121449186e-192

-2.5085439748189628e-58

-1.434935671644135e-62

-2.8036328029487993e-59

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	34
1	55	34
2	55	34

end0.0ms

sample7.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.439453%

Guaranteed chance to sample good point: 55.118931%

Results

1.2s	1794×	body	1280	invalid
835.0ms	7509×	body	80	valid
637.0ms	1363×	body	640	invalid
176.0ms	516×	body	320	invalid
92.0ms	131×	body	1280	valid
81.0ms	159×	body	640	valid
52.0ms	237×	body	160	invalid
48.0ms	124×	body	320	valid
43.0ms	351×	body	80	invalid
17.0ms	77×	body	160	valid

Details

sample4.2s

simplify395.0ms

prune19.0ms

localize43.0ms

rewrite23.0ms

series105.0ms

simplify83.0ms

prune125.0ms

localize16.0ms

rewrite18.0ms

series78.0ms

simplify81.0ms

prune125.0ms

localize24.0ms

rewrite19.0ms

series75.0ms

simplify82.0ms

prune145.0ms

localize25.0ms

rewrite19.0ms

series76.0ms

simplify84.0ms

prune95.0ms

regimes434.0ms

bsearch283.0ms

simplify2.0ms

end0.0ms

sample7.6s

Profiling