Details

Time bar (total: 6.3s)

sample349.0ms

Algorithm
intervals
Results
45.0ms72×body1280valid
23.0ms259×body80valid
15.0ms38×body640valid
4.0ms15×body320valid
2.0ms9×body160valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune15.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.6b

localize25.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (atan2 x.im x.re) y.re)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0b
(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.re)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(cos (+ (* (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:
17.0ms
(* (atan2 x.im x.re) y.re)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
158.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0205456
1546415
21264411
32748411
45001411

prune366.0ms

Filtered
78 candidates to 66 candidates (84.6%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.5b

localize16.0ms

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))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.7b
(* (atan2 x.im x.re) y.im)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

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)
5.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
91.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms
(* (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
0320595
11020544
23156516
35001484

prune309.0ms

Filtered
89 candidates to 70 candidates (78.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.0b

localize17.0ms

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))
0.2b
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
0.7b
(* (atan2 x.im x.re) y.im)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity
6×add-cube-cbrt add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×exp-prod
3×expm1-log1p-u associate-*r* associate-*l* log1p-expm1-u
2×rem-exp-log
1×exp-sum pow-prod-down prod-exp sum-log *-commutative cbrt-unprod fma-udef distribute-lft-out unswap-sqr
Counts
3 → 46
Calls
3 calls:
7.0ms
(exp (+ (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 0))
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)

series226.0ms

Counts
3 → 9
Calls
3 calls:
81.0ms
(exp (+ (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 0))
128.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
17.0ms
(* (atan2 x.im x.re) y.im)

simplify44.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 3 (39.0ms)

IterNodesCost
0156344
1478303
21498297
35001296

prune212.0ms

Filtered
55 candidates to 45 candidates (81.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
0.2b
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
0.7b
(* (atan2 x.im x.re) y.im)
0.7b
(* (atan2 x.im x.re) y.im)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 60
Calls
4 calls:
0.0ms
(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)
3.0ms
(* (atan2 x.im x.re) y.im)

series294.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
125.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
17.0ms
(* (atan2 x.im x.re) y.im)
19.0ms
(* (atan2 x.im x.re) y.im)

simplify72.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0118372
1347326
2879320
32273320
45001320

prune334.0ms

Filtered
72 candidates to 56 candidates (77.8%)
Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 3.0b

regimes150.0ms

Accuracy

0% (0.5b remaining)

Error of 4.3b against oracle of 3.8b and baseline of 4.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0238
1298
2298

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2068×body1280valid
684.0ms7915×body80valid
576.0ms1439×body640valid
175.0ms633×body320valid
58.0ms321×body160valid