Details

Time bar (total: 31.3s)

sample400.0ms

Algorithm
intervals
Results
125.0ms247×body80valid
88.0ms62×body1280valid
43.0ms45×body640valid
14.0ms21×body320valid
10.0ms3×body2560valid
4.0ms8×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize35.0ms

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)))

rewrite60.0ms

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:
7.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms
(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)))

series446.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
75.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
283.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.5s

Counts
68 → 68
Iterations

Useful iterations: 3 (393.0ms)

IterNodesCost
098845
1198787
2442699
3831686
41663686
54083686
done5001686

prune566.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.3b

localize36.0ms

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)))

rewrite254.0ms

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:
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
219.0ms
(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)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
72.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
233.0ms
(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 (207.0ms)

IterNodesCost
0731155
11501073
2293767
3578718
41509718
done5000718

prune671.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.3b

localize56.0ms

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)))

rewrite51.0ms

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:
12.0ms
(sin (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(sin (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
68.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.7s

Counts
64 → 64
Iterations

Useful iterations: 3 (180.0ms)

IterNodesCost
060791
1131707
2278635
3575615
41332615
53520615
done5001615

prune669.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.3b

localize43.0ms

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)))

rewrite39.0ms

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:
3.0ms
(log (exp (* (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)))
18.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
50.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
241.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.7s

Counts
64 → 64
Iterations

Useful iterations: done (4.7s)

IterNodesCost
090851
1166767
2331683
3667670
41490670
54145670
done5000668

prune528.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 20.3b

regimes562.0ms

Accuracy

79.7% (3.0b remaining)

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

bsearch283.0ms

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

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02965
13965
done3965

end0.0ms

sample9.0s

Algorithm
intervals
Results
3.8s2146×body1280valid
2.1s7903×body80valid
1.8s1397×body640valid
302.0ms560×body320valid
133.0ms38×body2560valid
87.0ms246×body160valid