Details

Time bar (total: 7.5s)

sample449.0ms

Algorithm
intervals
Results
40.0ms54×body640valid
39.0ms64×body1280valid
21.0ms254×body80valid
6.0ms2×body2560valid
4.0ms16×body320valid
1.0ms7×body160valid

simplify39.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117
done500117

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.8b

localize25.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

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×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
168.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415
done5003415

prune374.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.1b

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.im)
31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.5b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite47.0ms

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 sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+ hypot-def
Counts
4 → 68
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
168.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify110.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0263404
1755360
21828359
34355359
45001359
done5001359

prune406.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.re)
1.1b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.im)
36.5b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite48.0ms

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×sin-sum log-pow
Counts
4 → 71
Calls
4 calls:
8.0ms
(* (log (hypot x.re x.im)) y.re)
7.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
24.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (log (hypot x.re x.im)) y.re)
17.0ms
(* (atan2 x.im x.re) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
164.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify61.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0237414
1778363
22165361
35001361
done5001361

prune361.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

localize30.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
36.5b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))
36.5b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))
36.5b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sin-sum associate-*r* associate-*l*
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 50
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
23.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))
20.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))
21.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series508.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
166.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))
164.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))
160.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify52.0ms

Counts
62 → 62
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0127512
1339451
2720451
31332451
45001451
done5001451

prune333.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.0b

regimes261.0ms

Accuracy

0% (0.6b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03237
13637
23637
done3637

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.3s2192×body1280valid
662.0ms7963×body80valid
576.0ms1445×body640valid
151.0ms545×body320valid
57.0ms40×body2560valid
42.0ms236×body160valid