Details

Time bar (total: 10.8s)

sample450.0ms

Algorithm
intervals
Results
83.0ms85×body1280valid
43.0ms249×body80valid
29.0ms45×body640valid
5.0ms12×body320valid
4.0ms2×body2560valid
2.0ms8×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.1b

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
28.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite48.0ms

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:
10.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(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.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
146.0ms
(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

prune830.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.4b

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
28.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite44.0ms

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:
6.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
33.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
146.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify116.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0263404
1755360
21828359
34355359
45001359

prune716.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.2b

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
5.9b
(exp (log (hypot x.re x.im)))
31.0b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u exp-prod log1p-expm1-u add-log-exp
3×log-prod exp-sum
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow rem-exp-log
Counts
4 → 67
Calls
4 calls:
9.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(exp (log (hypot x.re x.im)))
19.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
45.0ms
(exp (log (hypot x.re x.im)))
143.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify67.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
0208362
1566317
21511317
32488313
45001313

prune692.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize31.0ms

Local error

Found 4 expressions with local error:

5.7b
(cbrt (atan2 x.im x.re))
5.7b
(cbrt (atan2 x.im x.re))
5.9b
(exp (log (hypot x.re x.im)))
31.0b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log expm1-log1p-u exp-prod add-cbrt-cube log1p-expm1-u add-log-exp
3×log-prod exp-sum
2×pow1/3
1×sin-sum log-pow rem-exp-log
Counts
4 → 53
Calls
4 calls:
3.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
3.0ms
(exp (log (hypot x.re x.im)))
20.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(cbrt (atan2 x.im x.re))
38.0ms
(cbrt (atan2 x.im x.re))
46.0ms
(exp (log (hypot x.re x.im)))
144.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify54.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 3 (14.0ms)

IterNodesCost
0128322
1231287
2405283
31082277
45001277

prune745.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

regimes679.0ms

Accuracy

0% (0.1b remaining)

Error of 3.2b against oracle of 3.1b and baseline of 3.2b

bsearch0.0ms

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03934
14134
24134

end0.0ms

sample5.1s

Algorithm
intervals
Results
2.2s2224×body1280valid
1.1s7994×body80valid
945.0ms1423×body640valid
237.0ms520×body320valid
85.0ms42×body2560valid
65.0ms216×body160valid