Details

Time bar (total: 1.4m)

sample344.0ms

Algorithm
intervals
Results
109.0ms247×body80valid
74.0ms62×body1280valid
39.0ms45×body640valid
13.0ms21×body320valid
11.0ms3×body2560valid
4.0ms8×body160valid

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
01937
13637
219636
3334936
done500036

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize80.0ms

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)))

rewrite90.0ms

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)))
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (atan2 x.im x.re) y.im)
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
261.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.7s

Counts
68 → 68
Iterations

Useful iterations: done (4.7s)

IterNodesCost
098845
1355787
done5000706

prune526.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.3b

localize71.0ms

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)))

rewrite195.0ms

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:
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
168.0ms
(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)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
285.0ms
(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)))

simplify10.9s

Counts
65 → 65
Iterations

Useful iterations: done (10.9s)

IterNodesCost
0731155
12341073
done5000748

prune595.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 20.2b

localize88.0ms

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)))

rewrite44.0ms

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:
16.0ms
(sin (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(sin (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
72.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify43.4s

Counts
64 → 64
Iterations

Useful iterations: 2 (21.4s)

IterNodesCost
060791
1231707
23971633
done5000633

prune689.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 20.2b

localize47.0ms

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)))

rewrite60.0ms

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)))
11.0ms
(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)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
240.0ms
(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
1286761
done5000690

prune570.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.2b

regimes590.0ms

Accuracy

79.6% (3.0b remaining)

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

bsearch301.0ms

Steps
ItersRangePoint
12
-3.2120421718303128e-288
1.4555397631981125e-288
-5.47990320893253e-309

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03066
13966
done3966

end0.0ms

sample8.6s

Algorithm
intervals
Results
3.4s2146×body1280valid
1.8s7903×body80valid
1.6s1397×body640valid
823.0ms560×body320valid
138.0ms38×body2560valid
80.0ms246×body160valid