Details

Time bar (total: 8.8s)

sample420.0ms

Algorithm
intervals
Results
69.0ms74×body1280valid
38.0ms256×body80valid
34.0ms57×body640valid
8.0ms18×body320valid
4.0ms2×body2560valid
2.0ms6×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite28.0ms

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)
13.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series246.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
150.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify80.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune386.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.6b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
31.9b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))
33.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite15.0ms

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

series227.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (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)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify91.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0259390
1727350
21728349
33565349
45002349

prune395.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.im)
1.0b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
31.9b
(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)))

series355.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(* (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)
153.0ms
(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 (17.0ms)

IterNodesCost
0223400
1696351
21619349
32891349
45001349

prune365.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.im)
1.0b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
32.0b
(sin (+ (* (* (log (hypot x.re x.im)) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im)) (* (atan2 x.im x.re) y.re)))

rewrite77.0ms

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:
0.0ms
(cbrt y.im)
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
70.0ms
(sin (+ (* (* (log (hypot x.re x.im)) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im)) (* (atan2 x.im x.re) y.re)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(cbrt y.im)
21.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
179.0ms
(sin (+ (* (* (log (hypot x.re x.im)) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im)) (* (atan2 x.im x.re) y.re)))

simplify163.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (38.0ms)

IterNodesCost
0207403
1587353
21469351
34371350
45001350

prune320.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.7b

regimes393.0ms

Accuracy

0% (0.7b remaining)

Error of 4.0b against oracle of 3.3b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02620
12620

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.9s2168×body1280valid
1.1s7914×body80valid
850.0ms1414×body640valid
248.0ms581×body320valid
71.0ms38×body2560valid
71.0ms235×body160valid