Details

Time bar (total: 8.7s)

sample389.0ms

Algorithm
intervals
Results
49.0ms58×body1280valid
37.0ms252×body80valid
24.0ms40×body640valid
6.0ms13×body320valid
2.0ms1×body2560valid
2.0ms7×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.1b

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
32.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
161.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify82.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune392.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.7b

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
32.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b
(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:
21.0ms
(* (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)))
157.0ms
(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 (19.0ms)

IterNodesCost
0259390
1731350
21732349
33569349
45002349

prune394.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.im)
1.2b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
33.2b
(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)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (log (hypot x.re x.im)) y.im)
16.0ms
(* (atan2 x.im x.re) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)
152.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0223400
1696351
21619349
32891349
45001349

prune384.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
1.2b
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
2.2b
(* (atan2 x.im x.re) y.im)
33.4b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-sqr-sqrt
9×add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cbrt-prod
2×*-commutative unswap-sqr
1×sin-sum pow1/3
Counts
4 → 64
Calls
4 calls:
0.0ms
(cbrt y.re)
10.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
3.0ms
(* (atan2 x.im x.re) y.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))))

series458.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(cbrt y.re)
82.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
16.0ms
(* (atan2 x.im x.re) y.im)
182.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify105.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
0245484
1824412
23545405
35002399

prune360.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.5b

regimes340.0ms

Accuracy

0% (0.6b remaining)

Error of 3.7b against oracle of 3.1b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03321
13721
23721

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.9s2225×body1280valid
1.1s7917×body80valid
814.0ms1371×body640valid
266.0ms603×body320valid
69.0ms243×body160valid
68.0ms37×body2560valid