Details

Time bar (total: 13.0s)

sample28.0ms

Algorithm
intervals
Results
13.0ms271×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11515
done1515

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
27.9b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 42
Calls
2 calls:
8.0ms
(+ (* x.re y.re) (* x.im y.im))
41.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series167.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(+ (* x.re y.re) (* x.im y.im))
112.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts
48 → 48
Iterations

Useful iterations: 3 (500.0ms)

IterNodesCost
086924
1232906
2767824
32337820
done5000820

prune272.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 27.5b

localize20.0ms

Local error

Found 2 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
27.9b
(/ (pow (+ (* x.re y.re) (* x.im y.im)) 1) (+ (* y.re y.re) (* y.im y.im)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
21×times-frac
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
7×add-exp-log associate-/l*
4×add-cbrt-cube add-log-exp sqr-pow
3×div-exp associate-/r*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative pow-to-exp frac-2neg pow-exp clear-num sum-log div-inv
Counts
2 → 58
Calls
2 calls:
14.0ms
(+ (* x.re y.re) (* x.im y.im))
42.0ms
(/ (pow (+ (* x.re y.re) (* x.im y.im)) 1) (+ (* y.re y.re) (* y.im y.im)))

series148.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(+ (* x.re y.re) (* x.im y.im))
110.0ms
(/ (pow (+ (* x.re y.re) (* x.im y.im)) 1) (+ (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts
64 → 64
Iterations

Useful iterations: 3 (710.0ms)

IterNodesCost
01221541
12751361
28931235
334721231
done50011231

prune234.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 27.5b

localize22.0ms

Local error

Found 3 expressions with local error:

0.5b
(/ (pow 1 1) (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im))))
0.7b
(+ (* y.re x.re) (* y.im x.im))
27.5b
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
99×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
48×unpow-prod-down
21×add-exp-log
19×associate-/r/
18×associate-/r*
16×sqr-pow
13×div-exp
11×flip3-+ flip-+
10×add-cbrt-cube div-inv associate-/l*
5×add-log-exp
4×cbrt-undiv pow-exp
3×pow1
2×pow-to-exp frac-2neg 1-exp clear-num associate-/l/
1×+-commutative sum-log
Counts
3 → 190
Calls
3 calls:
55.0ms
(/ (pow 1 1) (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im))))
14.0ms
(+ (* y.re x.re) (* y.im x.im))
45.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))

series344.0ms

Counts
3 → 9
Calls
3 calls:
201.0ms
(/ (pow 1 1) (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im))))
70.0ms
(+ (* y.re x.re) (* y.im x.im))
73.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))

simplify3.0s

Counts
199 → 199
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
03066534
15965517
213345101
339095041
done50005041

prune415.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 27.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
17.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.4b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.4b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
5×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 84
Calls
4 calls:
9.0ms
(+ (* x.re y.re) (* x.im y.im))
42.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
14.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(+ (* x.re y.re) (* x.im y.im))
151.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
55.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
56.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts
96 → 96
Iterations

Useful iterations: 3 (569.0ms)

IterNodesCost
01171780
12751649
27751541
320601525
done50001525

prune795.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 25.2b

regimes406.0ms

Accuracy

25% (2.2b remaining)

Error of 25.4b against oracle of 23.2b and baseline of 26.1b

bsearch5.0ms

simplify13.0ms

Iterations

Useful iterations: 3 (10.0ms)

IterNodesCost
02148
13046
23446
33845
done3845

end0.0ms

sample1.2s

Algorithm
intervals
Results
758.0ms8500×body80valid