Details

Time bar (total: 7.6s)

sample386.0ms

Algorithm
intervals
Results
54.0ms83×body1280valid
26.0ms259×body80valid
18.0ms43×body640valid
5.0ms17×body320valid
2.0ms11×body160valid
2.0ms1×body2560valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.4b

localize26.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.im)
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b
(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)))

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×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
1×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
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)))
9.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
166.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune406.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.6b

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+ hypot-def
Counts
4 → 68
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
158.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify104.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0259390
1731350
21732349
33569349
45002349

prune415.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.im)
1.4b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
31.6b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×pow1
10×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow
Counts
4 → 71
Calls
4 calls:
3.0ms
(* (log (hypot x.re x.im)) y.im)
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (log (hypot x.re x.im)) y.im)
16.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
153.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0223400
1696351
21619349
32891349
45001349

prune353.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im))))
1.4b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
31.4b
(sin (+ (* (* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×cbrt-prod
21×pow1
18×*-un-lft-identity
16×add-cube-cbrt
13×associate-*r* associate-*l*
10×add-exp-log
9×swap-sqr
8×add-cbrt-cube
6×pow1/3 log-pow unswap-sqr
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×prod-exp *-commutative cbrt-unprod
2×pow-sqr pow-prod-up
1×pow2 pow-plus sin-sum
Counts
4 → 97
Calls
4 calls:
7.0ms
(* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im))))
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
40.0ms
(sin (+ (* (* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

series345.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im))))
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
157.0ms
(sin (+ (* (* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

simplify108.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
0267826
1852743
23601688
35002684

prune412.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.2b

regimes390.0ms

Accuracy

0% (0.6b remaining)

Error of 3.9b against oracle of 3.3b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02620
12620

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.5s2280×body1280valid
706.0ms7893×body80valid
610.0ms1436×body640valid
171.0ms578×body320valid
83.0ms52×body2560valid
51.0ms265×body160valid