Details

Time bar (total: 7.2s)

sample361.0ms

Algorithm
intervals
Results
44.0ms68×body1280valid
22.0ms248×body80valid
19.0ms47×body640valid
5.0ms19×body320valid
1.0ms8×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.im)
28.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b
(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)))
10.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
164.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify82.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune413.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.3b

localize31.0ms

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)
28.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b
(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)
4.0ms
(* (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)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify112.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0263404
1755360
21828359
34355359
45001359

prune431.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

localize29.0ms

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)
5.8b
(exp (log (hypot x.re x.im)))
33.0b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

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:
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(exp (log (hypot x.re x.im)))
7.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
49.0ms
(exp (log (hypot x.re x.im)))
153.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
0208362
1566317
21248317
32201313
45001313

prune421.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.0b

localize31.0ms

Local error

Found 4 expressions with local error:

4.8b
(cbrt (atan2 x.im x.re))
4.8b
(cbrt (atan2 x.im x.re))
5.8b
(exp (log (hypot x.re x.im)))
33.0b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

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:
1.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
2.0ms
(exp (log (hypot x.re x.im)))
10.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series285.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(cbrt (atan2 x.im x.re))
39.0ms
(cbrt (atan2 x.im x.re))
49.0ms
(exp (log (hypot x.re x.im)))
151.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify53.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 3 (14.0ms)

IterNodesCost
0128322
1231287
2405283
31082277
45001277

prune367.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.0b

regimes349.0ms

Accuracy

0% (0.1b remaining)

Error of 3.5b against oracle of 3.4b and baseline of 3.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03834
14034
24034

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.4s2170×body1280valid
703.0ms7942×body80valid
572.0ms1376×body640valid
161.0ms573×body320valid
72.0ms47×body2560valid
44.0ms233×body160valid