Details

Time bar (total: 12.1s)

sample35.0ms

Algorithm
intervals
Results
19.0ms274×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: 25.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.2b
(+ (* x.re y.re) (* x.im y.im))
24.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite66.0ms

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:
9.0ms
(+ (* y.re y.re) (* y.im y.im))
14.0ms
(+ (* x.re y.re) (* x.im y.im))
42.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series235.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* y.re y.re) (* y.im y.im))
54.0ms
(+ (* x.re y.re) (* x.im y.im))
152.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify898.0ms

Counts
62 → 62
Iterations

Useful iterations: done (896.0ms)

IterNodesCost
0991090
12971067
21630953
done5001951

prune225.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
15.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite69.0ms

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))
35.0ms
(/ (+ (* 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)))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(+ (* x.re y.re) (* x.im y.im))
166.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
60.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify854.0ms

Counts
96 → 96
Iterations

Useful iterations: done (849.0ms)

IterNodesCost
01171780
12801649
211731543
done50001541

prune481.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 23.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.2b
(+ (* y.re x.re) (* y.im x.im))
0.5b
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im))))
24.3b
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
56×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
8×flip3-+ div-exp flip-+ add-log-exp
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv
2×+-commutative rec-exp frac-2neg 1-exp clear-num sum-log associate-/l/
1×pow-flip inv-pow
Counts
4 → 137
Calls
4 calls:
8.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(+ (* y.re x.re) (* y.im x.im))
35.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im))))
48.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ (* y.re y.re) (* y.im y.im))
39.0ms
(+ (* y.re x.re) (* y.im x.im))
188.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im))))
67.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))

simplify2.1s

Counts
149 → 149
Iterations

Useful iterations: 2 (590.0ms)

IterNodesCost
02043676
15873422
235663214
done50003214

prune470.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 23.0b

localize30.0ms

Local error

Found 4 expressions with local error:

9.8b
(cbrt (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im))))
24.3b
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))
24.3b
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))
24.3b
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
35×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×cbrt-prod
10×add-exp-log add-cbrt-cube
9×associate-/r* associate-/l*
8×associate-/r/
7×flip3-+ flip-+
6×associate-/l/
4×pow1 div-inv add-log-exp
3×cbrt-undiv frac-2neg div-exp clear-num
1×cbrt-div pow1/3
Counts
4 → 117
Calls
4 calls:
9.0ms
(cbrt (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im))))
47.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))
33.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))
72.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(cbrt (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im))))
67.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))
87.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))
103.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))

simplify2.5s

Counts
129 → 129
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01303037
13042984
210292765
347032752
done50002745

prune672.0ms

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 23.0b

regimes355.0ms

Accuracy

23.5% (2.3b remaining)

Error of 25.1b against oracle of 22.8b and baseline of 25.8b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01853
12253
done2253

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.2s8393×body80valid