Details

Time bar (total: 13.1s)

sample34.0ms

Algorithm
intervals
Results
15.0ms265×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11515
done1515

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
27.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite69.0ms

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:
11.0ms
(+ (* x.re y.re) (* x.im y.im))
56.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series158.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(+ (* 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)))

simplify1.6s

Counts
48 → 48
Iterations

Useful iterations: 3 (599.0ms)

IterNodesCost
086924
1232906
2767824
32337820
done5000820

prune137.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
16.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite324.0ms

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:
271.0ms
(+ (* 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)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ (* x.re y.re) (* x.im y.im))
143.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
49.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts
96 → 96
Iterations

Useful iterations: 3 (477.0ms)

IterNodesCost
01171780
12751649
27751541
320601525
done50001525

prune393.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 26.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
16.3b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
33.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×flip3-+ sqrt-div flip-+ add-log-exp
5×unswap-sqr
4×prod-exp
3×associate-*l*
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rec-exp 1-exp associate-*r/ pow-prod-down sum-log un-div-inv *-commutative div-inv
Counts
4 → 94
Calls
4 calls:
13.0ms
(+ (* x.re y.re) (* x.im y.im))
90.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
13.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* x.re y.re) (* x.im y.im))
156.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
51.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
52.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.6s

Counts
106 → 106
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01461886
13781642
211541474
337511458
done50011458

prune421.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 26.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.6b
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
0.7b
(+ (* x.re y.re) (* x.im y.im))
27.4b
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite100.0ms

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:
34.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
8.0ms
(+ (* x.re y.re) (* x.im y.im))
46.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series347.0ms

Counts
3 → 9
Calls
3 calls:
191.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
50.0ms
(+ (* x.re y.re) (* x.im y.im))
105.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify2.8s

Counts
135 → 135
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01943510
14683261
212712982
341252954
done50002954

prune353.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 26.2b

regimes229.0ms

Accuracy

0% (2.7b remaining)

Error of 25.8b against oracle of 23.1b and baseline of 25.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01325
11725
done1725

end0.0ms

sample1.2s

Algorithm
intervals
Results
719.0ms8453×body80valid