Details

Time bar (total: 7.4s)

sample436.0ms

Algorithm
intervals
Results
44.0ms259×body80valid
36.0ms57×body1280valid
16.0ms40×body640valid
4.0ms14×body320valid
2.0ms1×body2560valid
1.0ms7×body160valid

simplify36.0ms

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: 34.5b

localize26.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.re)
30.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite51.0ms

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:
6.0ms
(* (atan2 x.im x.re) y.re)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.re)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
172.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify77.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0211460
1555419
21277415
32762415
45002415
done5002415

prune370.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.2b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.im)
1.9b
(* (atan2 x.im x.re) y.re)
30.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.5b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite39.0ms

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:
6.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* (atan2 x.im x.re) y.re)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(sin (+ (* (log (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.im)
18.0ms
(* (atan2 x.im x.re) y.re)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
166.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify88.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0259390
1731350
21732349
33569349
45002349
done5002349

prune371.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.im)
1.9b
(* (atan2 x.im x.re) y.im)
1.9b
(* (atan2 x.im x.re) y.re)
33.5b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite38.0ms

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:
9.0ms
(* (log (hypot x.re x.im)) y.im)
6.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (log (hypot x.re x.im)) y.im)
18.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(* (atan2 x.im x.re) y.re)
160.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify73.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0223400
1696351
21619349
32891349
45001349
done5001349

prune353.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(log1p (sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re))))
1.9b
(* (atan2 x.im x.re) y.im)
1.9b
(* (atan2 x.im x.re) y.re)
33.5b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
5×expm1-log1p-u
4×log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×log1p-udef sin-sum log1p-expm1
Counts
4 → 61
Calls
4 calls:
0.0ms
(log1p (sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re))))
8.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
242.0ms
(log1p (sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re))))
17.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(* (atan2 x.im x.re) y.re)
160.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify56.0ms

Counts
73 → 73
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
0208433
1632378
22243378
35001377
done5001377

prune313.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.4b

regimes306.0ms

Accuracy

0% (0.7b remaining)

Error of 3.7b against oracle of 2.9b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03221
13621
23621
done3621

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.3s2166×body1280valid
684.0ms7961×body80valid
582.0ms1453×body640valid
169.0ms598×body320valid
66.0ms43×body2560valid
36.0ms204×body160valid