Details

Time bar (total: 9.8s)

sample22.0ms

Algorithm
intervals
Results
9.0ms266×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: 28.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
28.4b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite44.0ms

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))
34.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series123.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(+ (* x.re y.re) (* x.im y.im))
88.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts
48 → 48
Iterations

Useful iterations: 3 (414.0ms)

IterNodesCost
086924
1232906
2767824
32337820
done5000820

prune135.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 28.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* 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))))
32.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite61.0ms

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:
8.0ms
(+ (* x.re y.re) (* x.im y.im))
33.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (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)))

series233.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(+ (* x.re y.re) (* x.im y.im))
119.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.4s

Counts
96 → 96
Iterations

Useful iterations: 3 (600.0ms)

IterNodesCost
01171780
12751649
27751541
320601525
done50001525

prune278.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 26.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
0.6b
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
28.0b
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
55×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×associate-/r*
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp
7×flip3-+ flip-+
6×div-inv associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
2×rec-exp frac-2neg 1-exp clear-num associate-/l/
1×+-commutative pow-flip sum-log inv-pow
Counts
3 → 126
Calls
3 calls:
8.0ms
(+ (* x.re y.re) (* x.im y.im))
24.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
34.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series237.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(+ (* x.re y.re) (* x.im y.im))
139.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
62.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify1.9s

Counts
135 → 135
Iterations

Useful iterations: 3 (901.0ms)

IterNodesCost
01943510
14683261
212722982
341482954
done50012954

prune254.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 26.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))))
16.6b
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
32.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log
25×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
21×times-frac
18×sqrt-prod
15×add-cbrt-cube
10×sqrt-div div-exp
9×pow1 associate-/l*
7×associate-/r/
6×flip3-+ prod-exp flip-+
5×cbrt-undiv
4×associate-/r* add-log-exp
3×rec-exp 1-exp
2×frac-times rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 associate-*l/ clear-num cbrt-unprod div-inv associate-/l/
1×associate-*r/ pow-prod-down inv-pow
Counts
4 → 110
Calls
4 calls:
48.0ms
(/ 1 (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))))
25.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.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)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ 1 (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))))
85.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.3s

Counts
122 → 122
Iterations

Useful iterations: 3 (914.0ms)

IterNodesCost
01572812
13702308
210202070
332582006
done50022006

prune301.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 26.4b

regimes162.0ms

Accuracy

22.9% (2.4b remaining)

Error of 25.6b against oracle of 23.2b and baseline of 26.3b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01643
12043
done2043

end0.0ms

sample582.0ms

Algorithm
intervals
Results
282.0ms8444×body80valid