Details

Time bar (total: 7.1s)

sample384.0ms

Algorithm
intervals
Results
41.0ms68×body1280valid
23.0ms249×body80valid
18.0ms43×body640valid
6.0ms23×body320valid
2.0ms12×body160valid
2.0ms1×body2560valid

simplify47.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.2b

localize23.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
159.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune379.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

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)))
7.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
151.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify110.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0263404
1755360
21828359
34355359
45001359

prune386.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (* 1 (hypot x.re x.im))) y.re)
0.8b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
33.4b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
13×pow1
11×associate-*l*
10×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×prod-exp *-commutative cbrt-unprod unswap-sqr
2×log-pow
1×sin-sum
Counts
4 → 72
Calls
4 calls:
5.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
4.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
16.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
146.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify60.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0237443
1725387
22081380
35001378

prune348.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt y.re)
0.9b
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
1.7b
(* (atan2 x.im x.re) y.im)
33.5b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
11×add-sqr-sqrt
10×add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×pow-prod-down prod-exp cbrt-unprod
6×cbrt-prod
4×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×*-commutative
1×sin-sum pow1/3 unswap-sqr
Counts
4 → 69
Calls
4 calls:
1.0ms
(cbrt y.re)
10.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
3.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(cbrt y.re)
37.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
16.0ms
(* (atan2 x.im x.re) y.im)
174.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify39.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0279582
11168472
25001446

prune320.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

regimes272.0ms

Accuracy

0% (0.6b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03553
13753
23753

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.3s2156×body1280valid
695.0ms7910×body80valid
599.0ms1475×body640valid
151.0ms549×body320valid
63.0ms41×body2560valid
44.0ms242×body160valid