Details

Time bar (total: 8.9s)

sample412.0ms

Algorithm
intervals
Results
61.0ms66×body1280valid
37.0ms245×body80valid
26.0ms44×body640valid
7.0ms16×body320valid
2.0ms8×body160valid
2.0ms1×body2560valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.9b

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
28.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (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)))
165.0ms
(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

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.6b

localize25.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
28.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

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)))
5.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
152.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify91.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0259391
1731351
21732349
33569349
45002349

prune405.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.im)
1.5b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
31.8b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

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:
3.0ms
(* (log (hypot x.re x.im)) y.im)
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(* (log (hypot x.re x.im)) y.im)
16.0ms
(* (atan2 x.im x.re) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
153.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0223400
1696351
21619349
32891349
45001349

prune393.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.im)
1.5b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
31.7b
(sin (+ (* (* (log (hypot x.re x.im)) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im)) (* (atan2 x.im x.re) y.re)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum pow1/3
Counts
4 → 63
Calls
4 calls:
1.0ms
(cbrt y.im)
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
73.0ms
(sin (+ (* (* (log (hypot x.re x.im)) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im)) (* (atan2 x.im x.re) y.re)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(cbrt y.im)
17.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
177.0ms
(sin (+ (* (* (log (hypot x.re x.im)) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im)) (* (atan2 x.im x.re) y.re)))

simplify169.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (39.0ms)

IterNodesCost
0207403
1587353
21469351
34371350
45001350

prune331.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 4.0b

regimes444.0ms

Accuracy

0% (0.7b remaining)

Error of 3.7b against oracle of 3.0b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03423
13823
23823

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.9s2271×body1280valid
1.1s7972×body80valid
834.0ms1422×body640valid
228.0ms548×body320valid
69.0ms240×body160valid
64.0ms36×body2560valid