Details

Time bar (total: 15.5s)

sample39.0ms

Algorithm
intervals
Results
22.0ms272×body80valid

simplify7.0ms

Counts
1 → 1
Iterations
IterNodes
done15
115
011

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize24.0ms

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))
26.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
7×add-log-exp
5×add-cbrt-cube add-exp-log
4×flip3-+ flip-+
3×pow1 associate-/r* insert-posit16 associate-/l*
2×+-commutative sum-log associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
3 → 56
Calls
3 calls:
13.0ms
(+ (* y.re y.re) (* y.im y.im))
16.0ms
(+ (* x.re y.re) (* x.im y.im))
40.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series221.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(+ (* y.re y.re) (* y.im y.im))
52.0ms
(+ (* x.re y.re) (* x.im y.im))
116.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.8s

Counts
65 → 65
Iterations
IterNodes
done5034
34521
21139
1285
0101

prune418.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 25.8b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
16.8b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
5×flip3-+ flip-+
4×insert-posit16
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp div-inv
Counts
4 → 88
Calls
4 calls:
10.0ms
(+ (* x.re y.re) (* x.im y.im))
39.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(+ (* x.re y.re) (* x.im y.im))
174.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
65.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.1s

Counts
100 → 100
Iterations
IterNodes
done5005
32615
2905
1283
0120

prune591.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 24.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
16.9b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite121.0ms

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 insert-posit16
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 sum-log 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 98
Calls
4 calls:
17.0ms
(+ (* x.re y.re) (* x.im y.im))
62.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
15.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
21.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series319.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(+ (* x.re y.re) (* x.im y.im))
158.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
53.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
50.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.6s

Counts
110 → 110
Iterations
IterNodes
done5002
33857
21212
1403
0149

prune572.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 24.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
16.8b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×associate-/r* flip3-+ associate-/r/ flip-+
5×cbrt-undiv
4×cbrt-unprod insert-posit16 add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 164
Calls
4 calls:
122.0ms
(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
39.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
20.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
116.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
43.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.9s

Counts
176 → 176
Iterations
IterNodes
done5000
21906
1597
0196

prune792.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 24.1b

regimes379.0ms

Accuracy

0% (2.6b remaining)

Error of 25.5b against oracle of 22.9b and baseline of 25.5b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done17
117
013

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.0s8467×body80valid