Details

Time bar (total: 7.2s)

sample368.0ms

Algorithm
intervals
Results
54.0ms88×body1280valid
23.0ms247×body80valid
17.0ms43×body640valid
6.0ms21×body320valid
3.0ms2×body2560valid
1.0ms6×body160valid

simplify47.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.8b

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
31.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite22.0ms

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.im)
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)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
146.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify75.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0196425
1506388
21139386
32509386
45001386

prune335.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.8b

localize26.0ms

Local error

Found 4 expressions with local error:

4.8b
(cbrt (atan2 x.im x.re))
31.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

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))
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)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(cbrt (atan2 x.im x.re))
140.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify65.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 4 (60.0ms)

IterNodesCost
0160405
1334373
2731371
31992371
45002369

prune339.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.8b

localize27.0ms

Local error

Found 4 expressions with local error:

33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
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)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series147.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify145.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 5 (140.0ms)

IterNodesCost
089400
1215388
2503388
31265388
44227388
55002384

prune449.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.8b

localize35.0ms

Local error

Found 4 expressions with local error:

31.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
13×add-sqr-sqrt
12×sqrt-prod
11×add-cube-cbrt *-un-lft-identity
6×pow1 unpow-prod-down sqrt-div cube-prod
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ flip-+
2×cube-div rem-sqrt-square cbrt-div sqrt-pow1 pow1/2
1×cube-mult sin-sum pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 67
Calls
4 calls:
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)))
6.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series251.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify58.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0240553
1629526
21964526
35001526

prune397.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.8b

regimes358.0ms

Accuracy

77.8% (3.1b remaining)

Error of 22.7b against oracle of 19.6b and baseline of 33.5b

bsearch141.0ms

Steps
ItersRangePoint
9
-6.910543628884414e-298
-1.9551681257519828e-307
-2.01028984079832e-307

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04650
14650

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.4s2232×body1280valid
695.0ms7957×body80valid
572.0ms1379×body640valid
156.0ms559×body320valid
73.0ms48×body2560valid
42.0ms227×body160valid