Details

Time bar (total: 6.9s)

sample357.0ms

Algorithm
intervals
Results
47.0ms80×body1280valid
23.0ms247×body80valid
19.0ms48×body640valid
5.0ms18×body320valid
3.0ms14×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize25.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
31.1b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite24.0ms

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)
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
136.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms
(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

prune393.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.8b

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)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite23.0ms

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)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(exp (- (* (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)
16.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify65.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0308585
1921522
22504484
35002467

prune367.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

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)
1.6b
(* (atan2 x.im x.re) y.im)

rewrite9.0ms

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)
4.0ms
(* (atan2 x.im x.re) y.im)

series559.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(cbrt y.re)
186.0ms
(cbrt y.re)
179.0ms
(cbrt y.re)
17.0ms
(* (atan2 x.im x.re) y.im)

simplify56.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (19.0ms)

IterNodesCost
0102209
1300190
2710184
31530181
45001181

prune341.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
4.8b
(cbrt (atan2 x.im x.re))
4.8b
(cbrt (atan2 x.im x.re))
4.8b
(cbrt (atan2 x.im x.re))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
6.0ms
(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
1.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))

series175.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
44.0ms
(cbrt (atan2 x.im x.re))
39.0ms
(cbrt (atan2 x.im x.re))
44.0ms
(cbrt (atan2 x.im x.re))

simplify81.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
088456
1355404
22581372
35002365

prune376.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

regimes282.0ms

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
03426
13826
23826

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2070×body1280valid
694.0ms7983×body80valid
564.0ms1420×body640valid
172.0ms634×body320valid
53.0ms297×body160valid