Details

Time bar (total: 7.3s)

sample23.0ms

Algorithm
intervals
Results
12.0ms272×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
11515
done1515

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.3b
(+ (* x.re y.re) (* x.im y.im))
25.0b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

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
4×flip3-+ flip-+
3×pow1 associate-/r* associate-/l*
2×+-commutative sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 53
Calls
3 calls:
2.0ms
(+ (* y.re y.re) (* y.im y.im))
2.0ms
(+ (* x.re y.re) (* x.im y.im))
11.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series141.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* y.re y.re) (* y.im y.im))
31.0ms
(+ (* x.re y.re) (* x.im y.im))
83.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts
62 → 62
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
0991090
12701067
2965951
33918951
done5001951

prune190.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (* x.re y.re) (* x.im y.im))
16.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite27.0ms

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:
2.0ms
(+ (* x.re y.re) (* x.im y.im))
15.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* x.re y.re) (* x.im y.im))
109.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify981.0ms

Counts
96 → 96
Iterations

Useful iterations: 3 (336.0ms)

IterNodesCost
01171780
12741649
27681541
322691525
done50011525

prune299.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (* x.re y.re) (* x.im y.im))
25.0b
(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-div
10×add-sqr-sqrt flip3-+ flip-+
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity associate-/r/
6×pow1 sqrt-prod add-log-exp
4×frac-times
3×times-frac associate-/l*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ div-exp associate-*l/ associate-/l/
1×+-commutative frac-2neg prod-exp clear-num associate-/r* sum-log cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
2.0ms
(+ (* x.re y.re) (* x.im y.im))
16.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series191.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* x.re y.re) (* x.im y.im))
83.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
42.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify962.0ms

Counts
84 → 84
Iterations

Useful iterations: 3 (291.0ms)

IterNodesCost
01131662
12941304
28751142
325701110
done50001110

prune239.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.6b

localize17.0ms

Local error

Found 4 expressions with local error:

16.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

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
5×flip3-+ flip-+
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 88
Calls
4 calls:
11.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts
100 → 100
Iterations

Useful iterations: 3 (455.0ms)

IterNodesCost
01051833
12441680
26601570
319221548
done50001548

prune329.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.6b

regimes214.0ms

Accuracy

25.4% (2.2b remaining)

Error of 25.7b against oracle of 23.5b and baseline of 26.4b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01954
12554
done2554

end0.0ms

sample508.0ms

Algorithm
intervals
Results
294.0ms8482×body80valid