Details

Time bar (total: 11.3s)

sample39.0ms

Algorithm
intervals
Results
15.0ms271×body80valid

simplify8.0ms

Counts
1 → 1
Iterations
IterNodes
done15
115
011

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
22.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* flip3-+ flip-+ associate-/l*
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp div-inv
Counts
2 → 42
Calls
2 calls:
6.0ms
(+ (* x.re y.re) (* x.im y.im))
41.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series160.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(+ (* x.re y.re) (* x.im y.im))
104.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts
48 → 48
Iterations
IterNodes
done5001
34323
2906
1237
086

prune320.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
14.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite50.0ms

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-+
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 → 84
Calls
4 calls:
6.0ms
(+ (* x.re y.re) (* x.im y.im))
29.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ (* x.re y.re) (* x.im y.im))
129.0ms
(/ (+ (* 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)))
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts
96 → 96
Iterations
IterNodes
done5001
21173
1280
0117

prune624.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 19.6b

localize33.0ms

Local error

Found 4 expressions with local error:

14.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-div
12×add-sqr-sqrt
10×flip3-+ flip-+
9×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt sqrt-prod
8×associate-/r/
7×pow1
4×frac-times add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 associate-/l*
2×cbrt-undiv div-exp associate-*l/ associate-*r/ associate-/l/
1×clear-num associate-/r* frac-2neg prod-exp cbrt-unprod div-inv
Counts
4 → 76
Calls
4 calls:
60.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
46.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
53.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
48.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts
88 → 88
Iterations
IterNodes
done5000
32619
2812
1279
0107

prune489.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 19.6b

localize43.0ms

Local error

Found 4 expressions with local error:

14.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (cbrt (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re y.re) (* y.im y.im)))))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.8b
(cbrt (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re y.re) (* y.im y.im))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×cbrt-div sqrt-div
15×*-un-lft-identity flip3-+ add-cube-cbrt flip-+
12×times-frac
8×frac-times associate-/r/
6×pow1 add-exp-log sqrt-prod
5×cbrt-prod add-cbrt-cube
4×associate-/r* associate-*l/ associate-*r/ add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×cbrt-undiv clear-num frac-2neg pow1/3 cube-unmult div-exp rem-cbrt-cube div-inv
Counts
4 → 89
Calls
4 calls:
25.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (cbrt (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re y.re) (* y.im y.im)))))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.0ms
(cbrt (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re y.re) (* y.im y.im))))

series272.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (cbrt (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re y.re) (* y.im y.im)))))
50.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
48.0ms
(cbrt (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re y.re) (* y.im y.im))))

simplify1.1s

Counts
101 → 101
Iterations
IterNodes
done5000
21122
1348
0144

prune698.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 19.6b

regimes452.0ms

Accuracy

0% (3.1b remaining)

Error of 26.7b against oracle of 23.6b and baseline of 26.7b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done17
117
013

end0.0ms

sample1.3s

Algorithm
intervals
Results
917.0ms8463×body80valid