Details

sample4.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.125122%

Guaranteed chance to sample good point: 55.092126%

Results

38.0ms	47×	body	1280	invalid
30.0ms	247×	body	80	valid
27.0ms	51×	body	640	invalid
8.0ms	21×	body	320	invalid
6.0ms	13×	body	80	invalid
3.0ms	4×	body	1280	valid
2.0ms	4×	body	640	valid
2.0ms	1×	body	2560	invalid
1.0ms	5×	body	160	invalid
0.0ms	1×	body	160	valid

simplify393.0ms

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

prune30.0ms

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: 35.1b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.re)
32.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

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

series88.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
62.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify81.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	204	434
1	529	395
2	1179	392
3	2603	392
4	5002	392

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: 21.1b

Counts

70 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

6.0b	(cbrt (* (atan2 x.im x.re) y.re))
32.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

2.0ms	(cbrt (* (atan2 x.im x.re) y.re))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

series91.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt (* (atan2 x.im x.re) y.re))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 4 (65.0ms)

Iter	Nodes	Cost
0	203	533
1	412	478
2	856	471
3	2218	469
4	5002	467

prune104.0ms

Filtered

50 candidates to 59 candidates (-18.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	59	6	65

Merged error: 21.1b

Counts

65 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.re)
32.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

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×	`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.re)
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify80.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	204	434
1	529	395
2	1179	392
3	2603	392
4	5002	392

prune108.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	68	6	74

Merged error: 21.1b

Counts

74 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

13.1b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
32.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

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

series122.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify53.0ms

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

prune101.0ms

Filtered

56 candidates to 71 candidates (-26.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	71	6	77

Merged error: 21.1b

Counts

77 → 6

regimes371.0ms

Accuracy

77% (3.3b remaining)

Error of 22.8b against oracle of 19.6b and baseline of 33.7b

bsearch69.0ms

Steps

Iters	Range		Point
5	-8.803849925546127e-305	-3.2439133452398597e-305	-3.2976084584999315e-305

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35

end0.0ms

sample8.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.125122%

Guaranteed chance to sample good point: 55.092126%

Results

1.5s	1968×	body	1280	invalid
865.0ms	7562×	body	80	valid
658.0ms	1293×	body	640	invalid
161.0ms	440×	body	320	invalid
92.0ms	126×	body	1280	valid
77.0ms	159×	body	640	valid
75.0ms	40×	body	2560	invalid
46.0ms	381×	body	80	invalid
44.0ms	190×	body	160	invalid
34.0ms	96×	body	320	valid
14.0ms	57×	body	160	valid

Details

sample4.4s

simplify393.0ms

prune30.0ms

localize24.0ms

rewrite21.0ms

series88.0ms

simplify81.0ms

prune125.0ms

localize28.0ms

rewrite20.0ms

series91.0ms

simplify72.0ms

prune104.0ms

localize25.0ms

rewrite18.0ms

series74.0ms

simplify80.0ms

prune108.0ms

localize25.0ms

rewrite20.0ms

series122.0ms

simplify53.0ms

prune101.0ms

regimes371.0ms

bsearch69.0ms

simplify2.0ms

end0.0ms

sample8.1s

Profiling