Details

Time bar (total: 7.2s)

sample420.0ms

Algorithm
intervals
Results
57.0ms65×body1280valid
22.0ms257×body80valid
18.0ms48×body640valid
7.0ms25×body320valid
2.0ms10×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize24.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
30.5b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite53.0ms

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:
8.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
14.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
158.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
56.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify81.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411

prune360.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.4b

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)
1.8b
(* (atan2 x.im x.re) y.im)
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite39.0ms

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:
11.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
12.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series272.0ms

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))
91.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify84.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0320595
11020544
23156516
35001484

prune308.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.6b
(cbrt y.re)
0.6b
(cbrt y.re)
1.8b
(* (atan2 x.im x.re) y.im)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×cbrt-prod add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* associate-*l*
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 59
Calls
4 calls:
1.0ms
(cbrt y.re)
1.0ms
(cbrt y.re)
3.0ms
(cbrt y.re)
7.0ms
(* (atan2 x.im x.re) y.im)

series530.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(cbrt y.re)
170.0ms
(cbrt y.re)
169.0ms
(cbrt y.re)
18.0ms
(* (atan2 x.im x.re) y.im)

simplify58.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (18.0ms)

IterNodesCost
0102209
1300190
2710184
31530181
45001181

prune300.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.6b
(cbrt y.re)
0.6b
(cbrt y.re)
1.8b
(* (atan2 x.im x.re) y.im)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×cbrt-prod add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* associate-*l*
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 59
Calls
4 calls:
1.0ms
(cbrt y.re)
1.0ms
(cbrt y.re)
1.0ms
(cbrt y.re)
7.0ms
(* (atan2 x.im x.re) y.im)

series544.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(cbrt y.re)
175.0ms
(cbrt y.re)
176.0ms
(cbrt y.re)
18.0ms
(* (atan2 x.im x.re) y.im)

simplify54.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (18.0ms)

IterNodesCost
0102209
1300190
2710184
31530181
45001181

prune326.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.5b

regimes172.0ms

Accuracy

0% (0.6b remaining)

Error of 4.1b against oracle of 3.6b and baseline of 4.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03125
13525
23525

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s2032×body1280valid
651.0ms7973×body80valid
563.0ms1520×body640valid
171.0ms663×body320valid
60.0ms340×body160valid