Details

Time bar (total: 6.7s)

sample365.0ms

Algorithm
intervals
Results
37.0ms62×body1280valid
24.0ms264×body80valid
22.0ms56×body640valid
6.0ms22×body320valid
2.0ms12×body160valid

simplify37.0ms

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: 32.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (atan2 x.im x.re) y.im)
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b
(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.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)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(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)))

simplify81.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411

prune383.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 17.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (atan2 x.im x.re) y.re)
0.5b
(* (atan2 x.im x.re) y.im)
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square cos-sum sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
Counts
4 → 68
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
146.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify93.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0253386
1722346
21719345
33543345
45002345

prune372.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (hypot x.re x.im)) y.im)
0.5b
(* (atan2 x.im x.re) y.re)
0.5b
(* (atan2 x.im x.re) y.im)
33.7b
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×pow1
10×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum log-pow
Counts
4 → 71
Calls
4 calls:
3.0ms
(* (log (hypot x.re x.im)) y.im)
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (log (hypot x.re x.im)) y.im)
21.0ms
(* (atan2 x.im x.re) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
145.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify74.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0220396
1690347
21609345
32876345
45001345

prune334.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.5b

localize23.0ms

Local error

Found 4 expressions with local error:

3.5b
(cbrt (atan2 x.im x.re))
3.5b
(cbrt (atan2 x.im x.re))
3.5b
(cbrt (atan2 x.im x.re))
33.5b
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×cos-sum
Counts
4 → 49
Calls
4 calls:
0.0ms
(cbrt (atan2 x.im x.re))
0.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
7.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

series274.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(cbrt (atan2 x.im x.re))
40.0ms
(cbrt (atan2 x.im x.re))
40.0ms
(cbrt (atan2 x.im x.re))
148.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

simplify199.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
089404
1170360
2350354
31161354
44969354
55001354

prune283.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.5b

regimes208.0ms

Accuracy

0% (0.2b remaining)

Error of 2.9b against oracle of 2.7b and baseline of 2.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03131
13131

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s1989×body1280valid
702.0ms8076×body80valid
553.0ms1408×body640valid
168.0ms614×body320valid
56.0ms294×body160valid