Details

Time bar (total: 9.0s)

sample25.0ms

Algorithm
intervals
Results
11.0ms280×body80valid

simplify45.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11915
23615
34815
46615
57015
done7015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.3b
(- (* x.im y.re) (* x.re y.im))
24.8b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 55
Calls
3 calls:
8.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(- (* x.im y.re) (* x.re y.im))
24.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series162.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* y.re y.re) (* y.im y.im))
42.0ms
(- (* x.im y.re) (* x.re y.im))
92.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts
64 → 64
Iterations

Useful iterations: 2 (142.0ms)

IterNodesCost
01021120
12901097
2959981
33121981
done5001981

prune172.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* x.im y.re) (* x.re y.im))
15.1b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite52.0ms

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
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
7.0ms
(- (* x.im y.re) (* x.re y.im))
27.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (* x.im y.re) (* x.re y.im))
120.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts
98 → 98
Iterations

Useful iterations: 3 (451.0ms)

IterNodesCost
01211814
13061682
28881574
325391558
done50011558

prune268.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* x.im y.re) (* x.re y.im))
24.8b
(/ (- (* x.im y.re) (* x.re y.im)) (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-div
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity flip3-+ associate-/r/ flip-+
6×pow1 sqrt-prod add-log-exp
4×frac-times
3×times-frac associate-/l*
2×cbrt-undiv rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ div-exp associate-*l/ flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 74
Calls
4 calls:
7.0ms
(- (* x.im y.re) (* x.re y.im))
36.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
10.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series202.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (* x.im y.re) (* x.re y.im))
90.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts
86 → 86
Iterations

Useful iterations: 3 (621.0ms)

IterNodesCost
01161712
13291334
210651158
336221126
done50001126

prune233.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 22.3b

localize15.0ms

Local error

Found 4 expressions with local error:

15.1b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
21×sqrt-prod
18×times-frac
8×sqrt-div
7×pow1
6×add-exp-log associate-/r* add-cbrt-cube
4×flip3-+ flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp clear-num flip-- div-inv
Counts
4 → 89
Calls
4 calls:
25.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
9.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts
101 → 101
Iterations

Useful iterations: 3 (340.0ms)

IterNodesCost
01081859
12711705
27491595
320071573
done50001573

prune318.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 22.3b

regimes126.0ms

Accuracy

0% (3.0b remaining)

Error of 25.9b against oracle of 22.9b and baseline of 25.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01325
11625
done1625

end0.0ms

sample580.0ms

Algorithm
intervals
Results
278.0ms8467×body80valid