Details

Time bar (total: 7.0s)

sample363.0ms

Algorithm
intervals
Results
50.0ms84×body1280valid
21.0ms248×body80valid
18.0ms41×body640valid
3.0ms11×body320valid
1.0ms6×body160valid

simplify39.0ms

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: 33.5b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.im)
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.7b
(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)
3.0ms
(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)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
160.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune402.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.7b
(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)
3.0ms
(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)))

series226.0ms

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)))
158.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify95.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0259390
1731350
21732349
33569349
45002349

prune404.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (* 1 (hypot x.re x.im))) y.re)
0.6b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
35.7b
(sin (+ (* (log (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)
8.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
16.0ms
(* (atan2 x.im x.re) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)
150.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify61.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0237429
1729375
22088368
35001366

prune392.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

localize27.0ms

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))
35.7b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite10.0ms

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:
1.0ms
(cbrt (* (atan2 x.im x.re) y.im))
1.0ms
(cbrt (* (atan2 x.im x.re) y.im))
1.0ms
(cbrt (* (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)))

series333.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(cbrt (* (atan2 x.im x.re) y.im))
61.0ms
(cbrt (* (atan2 x.im x.re) y.im))
57.0ms
(cbrt (* (atan2 x.im x.re) y.im))
154.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify117.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 4 (24.0ms)

IterNodesCost
0122349
1194310
2336292
3770286
42708283
55001283

prune282.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

regimes288.0ms

Accuracy

0% (0.1b remaining)

Error of 3.8b against oracle of 3.7b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03427
13827
23827

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.4s2175×body1280valid
679.0ms7893×body80valid
536.0ms1341×body640valid
162.0ms571×body320valid
60.0ms40×body2560valid
44.0ms226×body160valid