Details

Time bar (total: 20.5s)

sample415.0ms

Algorithm
intervals
Results
120.0ms247×body80valid
87.0ms62×body1280valid
42.0ms45×body640valid
15.0ms21×body320valid
9.0ms3×body2560valid
3.0ms8×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize58.0ms

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)))

rewrite67.0ms

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)
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (atan2 x.im x.re) y.im)
62.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
243.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.9s

Counts
68 → 68
Iterations

Useful iterations: 3 (358.0ms)

IterNodesCost
098845
1198787
2442699
3831686
41663686
54083686
done5001686

prune631.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.3b

localize84.0ms

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)))

rewrite312.0ms

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)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
264.0ms
(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)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
198.0ms
(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)))

simplify1.7s

Counts
65 → 65
Iterations

Useful iterations: 3 (168.0ms)

IterNodesCost
0731155
11501073
2293767
3578718
41509718
done5000718

prune610.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.3b

localize67.0ms

Local error

Found 4 expressions with local error:

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)))

rewrite35.0ms

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

series336.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(sin (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
55.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.6s

Counts
64 → 64
Iterations

Useful iterations: 3 (140.0ms)

IterNodesCost
060791
1131707
2278635
3575615
41332615
53520615
done5001615

prune728.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.3b

localize55.0ms

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)))

rewrite70.0ms

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:
7.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
27.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
280.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.9s

Counts
64 → 64
Iterations

Useful iterations: done (3.9s)

IterNodesCost
090851
1166767
2331683
3667670
41490670
54145670
done5000668

prune473.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 20.3b

regimes643.0ms

bsearch3.0ms