Details

Time bar (total: 30.2s)

sample588.0ms

Algorithm
intervals
Results
227.0ms247×body80valid
116.0ms62×body1280valid
45.0ms21×body320valid
38.0ms45×body640valid
8.0ms3×body2560valid
3.0ms8×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize40.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.im)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite76.0ms

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×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
14.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
74.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
305.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.2s

Counts
68 → 68
Iterations

Useful iterations: 3 (276.0ms)

IterNodesCost
098845
1198787
2442699
3831686
41663686
54083686
done5001686

prune571.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.3b

localize73.0ms

Local error

Found 4 expressions with local error:

30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b
(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite281.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum
Counts
4 → 53
Calls
4 calls:
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
234.0ms
(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
265.0ms
(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts
65 → 65
Iterations

Useful iterations: 3 (211.0ms)

IterNodesCost
0731155
11501073
2293767
3578718
41509718
done5000718

prune571.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.3b

localize79.0ms

Local error

Found 4 expressions with local error:

24.8b
(sin (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 52
Calls
4 calls:
18.0ms
(sin (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(sin (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.6s

Counts
64 → 64
Iterations

Useful iterations: 3 (194.0ms)

IterNodesCost
060791
1131707
2278635
3575615
41332615
53520615
done5001615

prune698.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.3b

localize67.0ms

Local error

Found 4 expressions with local error:

4.7b
(log (exp (* (atan2 x.im x.re) y.im)))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-prod
5×add-log-exp
4×add-exp-log sqrt-div add-cbrt-cube
3×log-prod log-pow
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×exp-prod exp-to-pow sin-sum rem-log-exp
Counts
4 → 52
Calls
4 calls:
6.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series366.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
213.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.5s

Counts
64 → 64
Iterations

Useful iterations: done (3.5s)

IterNodesCost
090851
1166767
2331683
3667670
41490670
54145670
done5000668

prune532.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 20.3b

regimes600.0ms

Accuracy

79.7% (3.0b remaining)

Error of 22.0b against oracle of 19.0b and baseline of 33.7b

bsearch285.0ms

Steps
ItersRangePoint
12
-3.2120421718303128e-288
1.4555397631981125e-288
-3.5665767812761e-310

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02965
13965
done3965

end0.0ms

sample9.2s

Algorithm
intervals
Results
3.6s2146×body1280valid
2.2s7903×body80valid
1.8s1397×body640valid
512.0ms560×body320valid
100.0ms38×body2560valid
91.0ms246×body160valid