Details

Time bar (total: 9.0s)

sample451.0ms

Algorithm
intervals
Results
67.0ms78×body1280valid
22.0ms247×body80valid
19.0ms49×body640valid
5.0ms18×body320valid
2.0ms10×body160valid
2.0ms1×body2560valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (atan2 x.im x.re) y.im)
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

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:
7.0ms
(* (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)))
26.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
177.0ms
(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

prune404.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.0b

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (atan2 x.im x.re) y.re)
2.9b
(* (atan2 x.im x.re) y.im)
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b
(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:
7.0ms
(* (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)))
21.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
173.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify113.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0263404
1755360
21828359
34355359
45001359

prune413.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.re)
1.0b
(* (atan2 x.im x.re) y.re)
2.9b
(* (atan2 x.im x.re) y.im)
34.4b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×pow1
10×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow
Counts
4 → 71
Calls
4 calls:
8.0ms
(* (log (hypot x.re x.im)) y.re)
7.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
20.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (log (hypot x.re x.im)) y.re)
18.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
170.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify62.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0237414
1778363
22165361
35001361

prune374.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize26.0ms

Local error

Found 4 expressions with local error:

4.5b
(cbrt (* (atan2 x.im x.re) y.im))
4.5b
(cbrt (* (atan2 x.im x.re) y.im))
4.5b
(cbrt (* (atan2 x.im x.re) y.im))
34.4b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite31.0ms

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:
4.0ms
(cbrt (* (atan2 x.im x.re) y.im))
3.0ms
(cbrt (* (atan2 x.im x.re) y.im))
3.0ms
(cbrt (* (atan2 x.im x.re) y.im))
20.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(cbrt (* (atan2 x.im x.re) y.im))
64.0ms
(cbrt (* (atan2 x.im x.re) y.im))
66.0ms
(cbrt (* (atan2 x.im x.re) y.im))
169.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 4 (37.0ms)

IterNodesCost
0126363
1213322
2374304
3870298
44895295
55001295

prune283.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

regimes224.0ms

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
03223
13623
23623

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.4s2222×body1280valid
678.0ms7935×body80valid
575.0ms1430×body640valid
155.0ms556×body320valid
74.0ms48×body2560valid
45.0ms252×body160valid