Details

sample452.0ms

Algorithm

intervals

Results

54.0ms	71×	body	1280	valid
30.0ms	256×	body	80	valid
20.0ms	40×	body	640	valid
10.0ms	29×	body	320	valid
2.0ms	9×	body	160	valid
2.0ms	1×	body	2560	valid

simplify41.0ms

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

prune25.0ms

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: 32.0b

Counts

2 → 2

localize33.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.re)
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(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.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)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.re)
45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
178.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify73.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	194	425
1	496	388
2	1117	386
3	2390	386
4	5002	386

prune439.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 19.7b

Counts

70 → 7

localize31.0ms

Local error

Found 4 expressions with local error:

28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(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)))

rewrite37.0ms

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)))
25.0ms	(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)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
158.0ms	(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)))

simplify64.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (58.0ms)

Iter	Nodes	Cost
0	148	607
1	303	551
2	643	551
3	1810	551
4	5001	548

prune624.0ms

Filtered

65 candidates to 55 candidates (15.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	65	7	72

Merged error: 19.7b

Counts

72 → 7

localize31.0ms

Local error

Found 4 expressions with local error:

28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.6b	(sin (+ (* (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

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

series510.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
157.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
155.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify161.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (52.0ms)

Iter	Nodes	Cost
0	142	553
1	288	487
2	611	487
3	1512	487
4	4748	486
5	5001	486

prune385.0ms

Filtered

51 candidates to 48 candidates (5.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	50	8	58

Merged error: 19.7b

Counts

58 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

12.7b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(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)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify151.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 4 (143.0ms)

Iter	Nodes	Cost
0	191	725
1	493	717
2	1262	717
3	4720	717
4	5001	647

prune400.0ms

Filtered

71 candidates to 54 candidates (23.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	70	9	79

Merged error: 19.7b

Counts

79 → 9

regimes526.0ms

Accuracy

63% (5.1b remaining)

Error of 24.6b against oracle of 19.5b and baseline of 33.3b

bsearch315.0ms

Steps

Iters	Range		Point
9	6.247741763499922e-65	1.783555370542413e-59	6.71890239690567e-65
10	-0.00010039535931347623	-1.4806861344246088e-18	-1.5779631307095852e-18

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	69
1	54	69

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.7s	2270×	body	1280	valid
878.0ms	7983×	body	80	valid
712.0ms	1405×	body	640	valid
208.0ms	595×	body	320	valid
61.0ms	35×	body	2560	valid
58.0ms	252×	body	160	valid

Details

sample452.0ms

simplify41.0ms

prune25.0ms

localize33.0ms

rewrite21.0ms

series283.0ms

simplify73.0ms

prune439.0ms

localize31.0ms

rewrite37.0ms

series288.0ms

simplify64.0ms

prune624.0ms

localize31.0ms

rewrite23.0ms

series510.0ms

simplify161.0ms

prune385.0ms

localize30.0ms

rewrite20.0ms

series400.0ms

simplify151.0ms

prune400.0ms

regimes526.0ms

bsearch315.0ms

simplify2.0ms

end0.0ms

sample4.3s

Profiling