Details

Time bar (total: 8.2s)

sample392.0ms

Algorithm
intervals
Results
44.0ms57×body1280valid
34.0ms245×body80valid
33.0ms49×body640valid
7.0ms18×body320valid
3.0ms11×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
28.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

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)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify83.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0207454
1556413
21286411
32863411
45002411

prune388.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.1b

localize18.0ms

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)
2.2b
(* (atan2 x.im x.re) y.im)
28.0b
(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)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
89.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(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

prune335.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.6b
(cbrt y.re)
0.6b
(cbrt y.re)
2.2b
(* (atan2 x.im x.re) y.im)

rewrite5.0ms

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:
0.0ms
(cbrt y.re)
0.0ms
(cbrt y.re)
0.0ms
(cbrt y.re)
3.0ms
(* (atan2 x.im x.re) y.im)

series541.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(cbrt y.re)
175.0ms
(cbrt y.re)
175.0ms
(cbrt y.re)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify55.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (18.0ms)

IterNodesCost
0102209
1300190
2710184
31530181
45001181

prune322.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

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)
2.2b
(* (atan2 x.im x.re) y.im)

rewrite5.0ms

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:
0.0ms
(cbrt y.re)
0.0ms
(cbrt y.re)
0.0ms
(cbrt y.re)
3.0ms
(* (atan2 x.im x.re) y.im)

series544.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(cbrt y.re)
174.0ms
(cbrt y.re)
180.0ms
(cbrt y.re)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify55.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (19.0ms)

IterNodesCost
0102209
1300190
2710184
31530181
45001181

prune335.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

regimes219.0ms

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
03025
13425
23425

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.6s2101×body1280valid
1.1s7996×body80valid
804.0ms1456×body640valid
248.0ms635×body320valid
79.0ms301×body160valid