Details

Time bar (total: 8.0s)

sample434.0ms

Algorithm
intervals
Results
70.0ms80×body1280valid
44.0ms256×body80valid
31.0ms55×body640valid
8.0ms20×body320valid
4.0ms13×body160valid

simplify38.0ms

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: 30.5b

localize32.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (atan2 x.im x.re) y.im)
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b
(cos (+ (* (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×cos-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
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
144.0ms
(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 (14.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411

prune372.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.0b
(* (atan2 x.im x.re) y.im)
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×add-exp-log add-cbrt-cube
7×add-log-exp
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u
3×exp-prod exp-sum sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg rem-sqrt-square flip3-+ exp-diff diff-log prod-diff flip-+ hypot-def
Counts
4 → 79
Calls
4 calls:
8.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
86.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify64.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0308585
1921522
22504484
35002467

prune340.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
0.1b
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
2.0b
(* (atan2 x.im x.re) y.im)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
3×expm1-log1p-u exp-prod associate-*r* associate-*l* log1p-expm1-u
2×fma-udef
1×exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
3 → 44
Calls
3 calls:
1.0ms
(exp (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
0.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
3.0ms
(* (atan2 x.im x.re) y.im)

series218.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(exp (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
123.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
19.0ms
(* (atan2 x.im x.re) y.im)

simplify112.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
0154331
1426291
21148287
33857284
45001284

prune203.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
2.0b
(* (atan2 x.im x.re) y.im)
2.0b
(* (atan2 x.im x.re) y.im)
2.0b
(* (atan2 x.im x.re) y.im)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
10×pow1 add-exp-log add-cbrt-cube
9×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×pow1/3
Counts
4 → 73
Calls
4 calls:
0.0ms
(cbrt (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.im)

series293.0ms

Counts
4 → 12
Calls
4 calls:
245.0ms
(cbrt (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
16.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify64.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0215432
1623393
22358390
35001382

prune352.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.3b

regimes195.0ms

Accuracy

0% (0.6b remaining)

Error of 3.9b against oracle of 3.3b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02842
13242
23242

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.7s2146×body1280valid
1.3s7978×body80valid
831.0ms1442×body640valid
275.0ms655×body320valid
89.0ms303×body160valid