Details

Time bar (total: 9.1s)

sample398.0ms

Algorithm
intervals
Results
52.0ms78×body1280valid
38.0ms253×body80valid
32.0ms55×body640valid
7.0ms20×body320valid
1.0ms4×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.5b

localize26.0ms

Local error

Found 4 expressions with local error:

2.3b
(* (atan2 x.im x.re) y.im)
31.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.3b
(cos (+ (* (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×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)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(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)))

series256.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.im)
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
161.0ms
(cos (+ (* (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
0207454
1556413
21286411
32863411
45002411

prune395.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.3b
(* (atan2 x.im x.re) y.im)
31.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square flip3-- flip3-+ fma-neg diff-log prod-diff flip-- flip-+ hypot-def
Counts
4 → 77
Calls
4 calls:
3.0ms
(- (* (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)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
93.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
21.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify83.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0320596
11020545
23156516
35001484

prune348.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
0.0b
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
0.3b
(* (log (* 1 (hypot x.re x.im))) y.re)
2.3b
(* (atan2 x.im x.re) y.im)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity add-log-exp
8×add-exp-log associate-*l* add-cbrt-cube
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u
3×exp-prod exp-sum pow-prod-down
2×sub-neg diff-log prod-diff prod-exp log-pow *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×flip3-- exp-diff fma-neg flip--
Counts
4 → 76
Calls
4 calls:
11.0ms
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
4.0ms
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
7.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)

series371.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
141.0ms
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
106.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify104.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0269584
1861528
23384509
35001508

prune332.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (* 1 (hypot x.re x.im))) y.re)
2.3b
(* (atan2 x.im x.re) y.im)
2.3b
(* (atan2 x.im x.re) y.im)
2.3b
(* (atan2 x.im x.re) y.im)

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×pow1
14×associate-*l*
12×add-exp-log add-cube-cbrt *-un-lft-identity associate-*r* add-cbrt-cube
5×pow-prod-down
4×expm1-log1p-u prod-exp *-commutative cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
2×log-pow
Counts
4 → 82
Calls
4 calls:
7.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
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)

series162.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(* (atan2 x.im x.re) y.im)
22.0ms
(* (atan2 x.im x.re) y.im)

simplify1.6s

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0154379
1493330
21522323
34883321
45001321

prune402.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.6b

regimes158.0ms

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0208
1248
2248

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.3s1983×body1280valid
1.1s7978×body80valid
719.0ms1485×body640valid
227.0ms641×body320valid
69.0ms284×body160valid