Details

sample3.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.183105%

Guaranteed chance to sample good point: 64.693653%

Results

40.0ms	56×	body	1280	invalid
31.0ms	235×	body	80	valid
17.0ms	36×	body	640	invalid
6.0ms	17×	body	320	invalid
4.0ms	9×	body	640	valid
3.0ms	4×	body	1280	valid
2.0ms	8×	body	160	invalid
2.0ms	13×	body	80	invalid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify394.0ms

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: 35.4b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.im)
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.1b	(cos (+ (* (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×	`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)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series90.0ms

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)))
72.0ms	(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	5001	387

prune119.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 21.8b

Counts

70 → 5

localize15.0ms

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)
1.2b	(* (atan2 x.im x.re) y.im)
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

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:

3.0ms	(- (* (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)
3.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
22.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (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 (25.0ms)

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

prune118.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 4.5b

Counts

83 → 8

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (log x.re) y.re)
1.2b	(* (atan2 x.im x.re) y.im)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`pow1` `associate-l`
6×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r*` `add-cbrt-cube`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp` `unswap-sqr`
1×	`log-pow`

Counts

2 → 37

Calls

2 calls:

4.0ms	(* (log x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series16.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(* (log x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)

simplify113.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	142	156
1	491	135
2	1219	128
3	3534	128
4	5001	128

prune69.0ms

Filtered

26 candidates to 43 candidates (-65.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	43	8	51

Merged error: 4.5b

Counts

51 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.im)
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.1b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

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)))

series69.0ms

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)))
52.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

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

prune94.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	3	2	5
Picked	0	1	1
Done	0	2	2
Total	68	8	76

Merged error: 4.5b

Counts

76 → 8

regimes431.0ms

Accuracy

68.3% (5.2b remaining)

Error of 8.8b against oracle of 3.7b and baseline of 20.0b

bsearch82.0ms

Steps

Iters	Range		Point
9	-2.39638253738344e-305	1.5904371949932397e-304	3.2929543682718e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	35	15
2	35	15

end0.0ms

sample7.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.183105%

Guaranteed chance to sample good point: 64.693653%

Results

1.3s	1802×	body	1280	invalid
830.0ms	7534×	body	80	valid
612.0ms	1261×	body	640	invalid
192.0ms	573×	body	320	invalid
98.0ms	140×	body	1280	valid
76.0ms	160×	body	640	valid
52.0ms	415×	body	80	invalid
52.0ms	236×	body	160	invalid
39.0ms	106×	body	320	valid
14.0ms	60×	body	160	valid

Details

sample3.5s

simplify394.0ms

prune20.0ms

localize23.0ms

rewrite20.0ms

series90.0ms

simplify82.0ms

prune119.0ms

localize15.0ms

rewrite19.0ms

series70.0ms

simplify81.0ms

prune118.0ms

localize13.0ms

rewrite8.0ms

series16.0ms

simplify113.0ms

prune69.0ms

localize25.0ms

rewrite18.0ms

series69.0ms

simplify79.0ms

prune94.0ms

regimes431.0ms

bsearch82.0ms

simplify2.0ms

end0.0ms

sample7.0s

Profiling