Details

Time bar (total: 7.4s)

sample365.0ms

Algorithm
intervals
Results
43.0ms69×body1280valid
24.0ms263×body80valid
22.0ms55×body640valid
5.0ms17×body320valid
2.0ms11×body160valid
1.0ms1×body2560valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (atan2 x.im x.re) y.im)
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b
(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)))
3.0ms
(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)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
162.0ms
(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

prune402.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (atan2 x.im x.re) y.re)
0.5b
(* (atan2 x.im x.re) y.im)
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b
(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
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)
3.0ms
(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)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
152.0ms
(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

prune414.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (* 1 (hypot x.re x.im))) y.re)
0.5b
(* (atan2 x.im x.re) y.re)
0.5b
(* (atan2 x.im x.re) y.im)
33.7b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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

series286.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (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)
154.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify63.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0237443
1725387
22081380
35001378

prune384.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (log (* 1 (hypot x.re x.im))) y.re))
0.6b
(cbrt (* (log (* 1 (hypot x.re x.im))) y.re))
0.6b
(cbrt (* (log (* 1 (hypot x.re x.im))) y.re))
33.7b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3
1×sin-sum
Counts
4 → 43
Calls
4 calls:
2.0ms
(cbrt (* (log (* 1 (hypot x.re x.im))) y.re))
2.0ms
(cbrt (* (log (* 1 (hypot x.re x.im))) y.re))
2.0ms
(cbrt (* (log (* 1 (hypot x.re x.im))) y.re))
7.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series631.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(cbrt (* (log (* 1 (hypot x.re x.im))) y.re))
162.0ms
(cbrt (* (log (* 1 (hypot x.re x.im))) y.re))
161.0ms
(cbrt (* (log (* 1 (hypot x.re x.im))) y.re))
150.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 3 (17.0ms)

IterNodesCost
0138453
1245403
2567388
31656373
45001373

prune328.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.6b

regimes330.0ms

Accuracy

0% (0.1b remaining)

Error of 3.0b against oracle of 2.9b and baseline of 3.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03332
13532
23532

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s2157×body1280valid
702.0ms8048×body80valid
554.0ms1370×body640valid
153.0ms530×body320valid
68.0ms45×body2560valid
42.0ms231×body160valid