Details

Time bar (total: 7.6s)

sample430.0ms

Algorithm
intervals
Results
62.0ms68×body1280valid
23.0ms256×body80valid
14.0ms35×body640valid
4.0ms15×body320valid
3.0ms2×body2560valid
1.0ms7×body160valid

simplify38.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117
done500117

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.7b

localize23.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.im)
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(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)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(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)))

simplify79.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415
done5003415

prune385.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.4b

localize25.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.re)
1.4b
(* (atan2 x.im x.re) y.im)
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite44.0ms

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)
6.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms
(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:
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)))
164.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify108.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0263404
1755360
21828359
34355359
45001359
done5001359

prune419.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (* 1 (hypot x.re x.im))) y.re)
1.3b
(* (atan2 x.im x.re) y.re)
1.4b
(* (atan2 x.im x.re) y.im)
30.6b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

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.re)
7.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
20.0ms
(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:
108.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
17.0ms
(* (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)))

simplify60.0ms

Counts
84 → 84
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0237443
1725387
22081380
35001378
done5001378

prune385.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
1.3b
(* (atan2 x.im x.re) y.re)
1.4b
(* (atan2 x.im x.re) y.im)
30.6b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum pow1/3
Counts
4 → 63
Calls
4 calls:
1.0ms
(cbrt y.re)
7.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
22.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(cbrt y.re)
18.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (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)))

simplify131.0ms

Counts
75 → 75
Iterations

Useful iterations: 3 (34.0ms)

IterNodesCost
0206347
1576305
21398303
33669302
45002302
done5002302

prune345.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

regimes340.0ms

Accuracy

0% (0.3b remaining)

Error of 4.0b against oracle of 3.7b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03126
13326
23326
done3326

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.3s2191×body1280valid
671.0ms7935×body80valid
566.0ms1428×body640valid
149.0ms557×body320valid
96.0ms62×body2560valid
43.0ms231×body160valid