Details

Time bar (total: 10.1s)

sample428.0ms

Algorithm
intervals
Results
72.0ms78×body1280valid
41.0ms250×body80valid
31.0ms49×body640valid
7.0ms15×body320valid
2.0ms9×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.9b

localize31.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
28.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite44.0ms

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×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
141.0ms
(cos (+ (* (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
0207456
1556415
21286411
32863411
45002411

prune758.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.3b

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
28.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite39.0ms

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 cos-sum sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
Counts
4 → 68
Calls
4 calls:
6.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series193.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
129.0ms
(cos (+ (* (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
0253386
1722346
21719345
33543345
45002345

prune633.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.im)
1.4b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
31.0b
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite39.0ms

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×cos-sum log-pow
Counts
4 → 71
Calls
4 calls:
8.0ms
(* (log (hypot x.re x.im)) y.im)
6.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (log (hypot x.re x.im)) y.im)
14.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
131.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify72.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0220396
1690347
21609345
32876345
45001345

prune612.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (log (hypot x.re x.im)))
1.4b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
31.1b
(cos (+ (* (* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×cbrt-prod expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum pow1/3 log-pow
Counts
4 → 64
Calls
4 calls:
1.0ms
(cbrt (log (hypot x.re x.im)))
6.0ms
(* (atan2 x.im x.re) y.re)
9.0ms
(* (atan2 x.im x.re) y.im)
83.0ms
(cos (+ (* (* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(cbrt (log (hypot x.re x.im)))
15.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
130.0ms
(cos (+ (* (* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

simplify63.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
0200498
1530436
21204434
32104432
45002432

prune799.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.7b

regimes597.0ms

Accuracy

0% (0.6b remaining)

Error of 3.1b against oracle of 2.5b and baseline of 3.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03035
13035

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.9s2067×body1280valid
1.1s8008×body80valid
903.0ms1461×body640valid
264.0ms604×body320valid
78.0ms279×body160valid