Details

sample432.0ms

Algorithm

intervals

Results

41.0ms	47×	body	640	valid
38.0ms	57×	body	1280	valid
21.0ms	253×	body	80	valid
4.0ms	15×	body	320	valid
4.0ms	9×	body	160	valid
3.0ms	2×	body	2560	valid

simplify39.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.re)
29.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite53.0ms

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:

7.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (atan2 x.im x.re) y.re)
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
147.0ms	(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 (14.0ms)

Iter	Nodes	Cost
0	194	425
1	496	388
2	1117	386
3	2398	386
4	5002	386

prune331.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.8b

localize28.0ms

Local error

Found 4 expressions with local error:

29.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(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)))

rewrite157.0ms

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:

7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
133.0ms	(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)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
137.0ms	(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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	148	607
1	303	551
2	643	551
3	1821	551
4	5001	548

prune393.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.8b

localize26.0ms

Local error

Found 4 expressions with local error:

4.2b	(cbrt (atan2 x.im x.re))
29.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.8b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

series240.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(cbrt (atan2 x.im x.re))
31.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
137.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

simplify79.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (73.0ms)

Iter	Nodes	Cost
0	167	489
1	366	443
2	822	441
3	2327	441
4	5001	439

prune332.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
29.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.5b	(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) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`add-exp-log`
7×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`sqrt-prod`
4×	`sqrt-div` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

21.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms	(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) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify128.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (122.0ms)

Iter	Nodes	Cost
0	240	560
1	596	498
2	1516	494
3	4223	487
4	5001	486

prune327.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.8b

regimes313.0ms

Accuracy

79.4% (2.9b remaining)

Error of 23.0b against oracle of 20.2b and baseline of 34.1b

bsearch138.0ms

Steps

Iters	Range		Point
9	-3.8284825051561105e-306	7.462658039059417e-304	-5.108189418209377e-309

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	36
1	42	36

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2185×	body	1280	valid
667.0ms	7965×	body	80	valid
555.0ms	1363×	body	640	valid
159.0ms	579×	body	320	valid
72.0ms	46×	body	2560	valid
40.0ms	228×	body	160	valid