Details

Time bar (total: 6.4s)

sample368.0ms

Algorithm
intervals
Results
46.0ms74×body1280valid
21.0ms56×body640valid
21.0ms251×body80valid
4.0ms16×body320valid
2.0ms13×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.0b

localize24.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.im)
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b
(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)))
4.0ms
(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)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
153.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411

prune373.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.9b

localize15.0ms

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)
1.2b
(* (atan2 x.im x.re) y.im)
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite24.0ms

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

series230.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(exp (- (* (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)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify63.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0308585
1921522
22504484
35002467

prune336.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
0.0b
(exp (- (* (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)
1.2b
(* (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:
4.0ms
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
11.0ms
(exp (- (* (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)

series343.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
98.0ms
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
99.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify102.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0269584
1861528
23384509
35001508

prune317.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
4.0b
(cbrt (atan2 x.im x.re))
4.0b
(cbrt (atan2 x.im x.re))
4.0b
(cbrt (atan2 x.im x.re))

rewrite9.0ms

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)))
0.0ms
(cbrt (atan2 x.im x.re))
0.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))

series174.0ms

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))
38.0ms
(cbrt (atan2 x.im x.re))
43.0ms
(cbrt (atan2 x.im x.re))

simplify79.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
088456
1355404
22581372
35002365

prune327.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

regimes180.0ms

Accuracy

0% (0.5b remaining)

Error of 4.2b against oracle of 3.7b and baseline of 4.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02922
13322
23322

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s1987×body1280valid
683.0ms7946×body80valid
538.0ms1377×body640valid
171.0ms636×body320valid
48.0ms270×body160valid