Details

Time bar (total: 8.6s)

sample367.0ms

Algorithm
intervals
Results
45.0ms73×body1280valid
21.0ms257×body80valid
18.0ms44×body640valid
6.0ms23×body320valid
4.0ms2×body2560valid
2.0ms13×body160valid

simplify41.0ms

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: 34.5b

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.im)
30.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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)))

series254.0ms

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)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
163.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify83.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune415.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.1b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.re)
1.2b
(* (atan2 x.im x.re) y.im)
30.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b
(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)))
8.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
158.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify114.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0263404
1755360
21828359
34355359
45001359

prune419.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (* 1 (hypot x.re x.im))) y.re)
1.2b
(* (atan2 x.im x.re) y.re)
1.2b
(* (atan2 x.im x.re) y.im)
32.5b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

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:
8.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
5.0ms
(* (atan2 x.im x.re) 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) y.re)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
19.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
155.0ms
(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

prune377.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.0b

localize25.0ms

Local error

Found 4 expressions with local error:

9.1b
(cbrt (* (atan2 x.im x.re) y.re))
9.1b
(cbrt (* (atan2 x.im x.re) y.re))
9.1b
(cbrt (* (atan2 x.im x.re) y.re))
32.6b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (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 (* (atan2 x.im x.re) y.re))
1.0ms
(cbrt (* (atan2 x.im x.re) y.re))
2.0ms
(cbrt (* (atan2 x.im x.re) y.re))
13.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

series360.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(cbrt (* (atan2 x.im x.re) y.re))
61.0ms
(cbrt (* (atan2 x.im x.re) y.re))
58.0ms
(cbrt (* (atan2 x.im x.re) y.re))
183.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

simplify1.6s

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 4 (37.0ms)

IterNodesCost
0124489
1211430
2372412
3901406
44718403
55001403

prune280.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.0b

regimes228.0ms

Accuracy

0% (0.1b remaining)

Error of 3.6b against oracle of 3.5b and baseline of 3.6b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02717
12917
22917

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.4s2206×body1280valid
686.0ms7970×body80valid
587.0ms1451×body640valid
161.0ms573×body320valid
57.0ms38×body2560valid
37.0ms207×body160valid