Details

Time bar (total: 6.9s)

sample364.0ms

Algorithm
intervals
Results
47.0ms73×body1280valid
24.0ms260×body80valid
21.0ms50×body640valid
5.0ms17×body320valid
2.0ms1×body2560valid
1.0ms7×body160valid

simplify40.0ms

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: 33.7b

localize26.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.im)
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b
(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)))

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)))

series248.0ms

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)))
160.0ms
(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

prune382.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.0b

localize31.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b
(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:
4.0ms
(* (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)))
6.0ms
(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)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
148.0ms
(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

prune396.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (* 1 (hypot x.re x.im))) y.re)
1.6b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
33.2b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

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)
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
152.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (56.0ms)

IterNodesCost
0237443
1725387
22081380
35001378

prune364.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (* 1 (hypot x.re x.im))) y.re)
1.6b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
33.2b
(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)))

series281.0ms

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)
16.0ms
(* (atan2 x.im x.re) y.im)
151.0ms
(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

prune374.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.3b

regimes225.0ms

Accuracy

0% (0.1b remaining)

Error of 3.3b against oracle of 3.2b and baseline of 3.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03523
13923
23923

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.3s2143×body1280valid
702.0ms7995×body80valid
573.0ms1394×body640valid
152.0ms537×body320valid
58.0ms39×body2560valid
42.0ms228×body160valid