Details

Time bar (total: 7.1s)

sample366.0ms

Algorithm
intervals
Results
42.0ms68×body1280valid
24.0ms249×body80valid
18.0ms43×body640valid
6.0ms23×body320valid
2.0ms12×body160valid
2.0ms1×body2560valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.2b

localize26.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b
(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)))
8.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series256.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(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)))

simplify81.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune391.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b
(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)))

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)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
160.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify92.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0259390
1731350
21732349
33569349
45002349

prune397.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
5.7b
(exp (log (hypot x.re x.im)))
33.4b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite14.0ms

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)
1.0ms
(exp (log (hypot x.re x.im)))
5.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
51.0ms
(exp (log (hypot x.re x.im)))
157.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify59.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
0204348
1538307
21183307
32021303
45001303

prune370.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
1.7b
(* (atan2 x.im x.re) y.im)
5.7b
(exp (log (hypot x.re x.im)))
33.5b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
15×add-exp-log
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r*
7×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u exp-prod associate-*l* log1p-expm1-u add-log-exp
3×cbrt-prod log-prod exp-sum
2×*-commutative
1×sin-sum log-pow rem-exp-log unswap-sqr
Counts
4 → 73
Calls
4 calls:
34.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(exp (log (hypot x.re x.im)))
7.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series289.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
16.0ms
(* (atan2 x.im x.re) y.im)
52.0ms
(exp (log (hypot x.re x.im)))
183.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify74.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0287583
11100484
23753460
35001446

prune354.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

regimes275.0ms

Accuracy

0% (0.6b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03251
13251

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.4s2156×body1280valid
712.0ms7910×body80valid
618.0ms1475×body640valid
157.0ms549×body320valid
66.0ms41×body2560valid
51.0ms242×body160valid