Details

Time bar (total: 7.6s)

sample466.0ms

Algorithm
intervals
Results
72.0ms85×body1280valid
23.0ms250×body80valid
22.0ms54×body640valid
7.0ms24×body320valid
3.0ms15×body160valid
2.0ms1×body2560valid

simplify38.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117
done500117

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.7b

localize31.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (atan2 x.im x.re) y.im)
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite45.0ms

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

series267.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.im)
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
173.0ms
(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 (14.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415
done5003415

prune378.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.7b

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.re)
2.4b
(* (atan2 x.im x.re) y.im)
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.1b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite41.0ms

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)))
18.0ms
(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.re)
18.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
167.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify93.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0259390
1731350
21732349
33569349
45002349
done5002349

prune380.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.im)
1.5b
(* (atan2 x.im x.re) y.re)
2.4b
(* (atan2 x.im x.re) y.im)
35.1b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite41.0ms

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.im)
7.0ms
(* (atan2 x.im x.re) y.re)
9.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series305.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (log (hypot x.re x.im)) y.im)
18.0ms
(* (atan2 x.im x.re) y.re)
22.0ms
(* (atan2 x.im x.re) y.im)
160.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify74.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0223400
1696351
21619349
32891349
45001349
done5001349

prune382.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (log (hypot x.re x.im)))
1.5b
(* (atan2 x.im x.re) y.re)
2.4b
(* (atan2 x.im x.re) y.im)
34.8b
(sin (+ (* (* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×cbrt-prod expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum pow1/3 log-pow
Counts
4 → 64
Calls
4 calls:
1.0ms
(cbrt (log (hypot x.re x.im)))
7.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
85.0ms
(sin (+ (* (* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(cbrt (log (hypot x.re x.im)))
17.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
166.0ms
(sin (+ (* (* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im)))) (* (cbrt (log (hypot x.re x.im))) y.im)) (* (atan2 x.im x.re) y.re)))

simplify61.0ms

Counts
76 → 76
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
0205502
1538440
21216438
32129436
45001436
done5001436

prune346.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.1b

regimes402.0ms

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
03636
14036
24036
done4036

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.4s2234×body1280valid
698.0ms7938×body80valid
557.0ms1365×body640valid
152.0ms543×body320valid
66.0ms44×body2560valid
43.0ms238×body160valid