Details

Time bar (total: 7.8s)

sample440.0ms

Algorithm
intervals
Results
67.0ms76×body1280valid
24.0ms255×body80valid
15.0ms36×body640valid
5.0ms3×body2560valid
4.0ms16×body320valid
2.0ms7×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: 34.3b

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite50.0ms

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)))
25.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
174.0ms
(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

prune380.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.1b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.re)
1.4b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite42.0ms

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)))
20.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series244.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
169.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify112.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0263404
1755360
21828359
34355359
45001359
done5001359

prune388.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (* 1 (hypot x.re x.im))) y.im)
1.2b
(* (atan2 x.im x.re) y.re)
1.4b
(* (atan2 x.im x.re) y.im)
32.6b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
13×pow1
11×associate-*l*
10×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×prod-exp *-commutative cbrt-unprod unswap-sqr
2×log-pow
1×sin-sum
Counts
4 → 72
Calls
4 calls:
17.0ms
(* (log (* 1 (hypot x.re x.im))) y.im)
6.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
19.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (log (* 1 (hypot x.re x.im))) y.im)
18.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
163.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Counts
84 → 84
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0227443
1694387
22006380
35001378
done5001378

prune363.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (log (* 1 (hypot x.re x.im))))
1.2b
(* (atan2 x.im x.re) y.re)
1.4b
(* (atan2 x.im x.re) y.im)
33.0b
(sin (+ (* (* (cbrt (log (* 1 (hypot x.re x.im)))) (cbrt (log (* 1 (hypot x.re x.im))))) (* (cbrt (log (* 1 (hypot x.re x.im)))) y.im)) (* (atan2 x.im x.re) y.re)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
5×cbrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down
2×prod-exp log-pow *-commutative cbrt-unprod unswap-sqr
1×sin-sum pow1/3
Counts
4 → 65
Calls
4 calls:
3.0ms
(cbrt (log (* 1 (hypot x.re x.im))))
6.0ms
(* (atan2 x.im x.re) y.re)
8.0ms
(* (atan2 x.im x.re) y.im)
124.0ms
(sin (+ (* (* (cbrt (log (* 1 (hypot x.re x.im)))) (cbrt (log (* 1 (hypot x.re x.im))))) (* (cbrt (log (* 1 (hypot x.re x.im)))) y.im)) (* (atan2 x.im x.re) y.re)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(cbrt (log (* 1 (hypot x.re x.im))))
18.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
170.0ms
(sin (+ (* (* (cbrt (log (* 1 (hypot x.re x.im)))) (cbrt (log (* 1 (hypot x.re x.im))))) (* (cbrt (log (* 1 (hypot x.re x.im)))) y.im)) (* (atan2 x.im x.re) y.re)))

simplify63.0ms

Counts
77 → 77
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
0209568
1552498
21232495
32176492
45001492
done5001492

prune324.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.0b

regimes347.0ms

Accuracy

0% (0.6b remaining)

Error of 3.9b against oracle of 3.3b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03122
13322
23322
done3322

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.4s2307×body1280valid
703.0ms7933×body80valid
589.0ms1431×body640valid
163.0ms562×body320valid
78.0ms50×body2560valid
46.0ms247×body160valid