Details

Time bar (total: 18.0s)

sample28.0ms

Algorithm
intervals
Results
14.0ms272×body80valid

simplify69.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
011284
121259
240259
356259
476259
590259
694259
done94259

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* x.im y.re) (* x.re y.im))
23.2b
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite26.0ms

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* associate-/l*
2×expm1-log1p-u pow1 flip3-- log1p-expm1-u flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
2 → 48
Calls
2 calls:
6.0ms
(- (* x.im y.re) (* x.re y.im))
18.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series163.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(- (* x.im y.re) (* x.re y.im))
115.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.1s

Counts
54 → 54
Iterations

Useful iterations: done (2.1s)

IterNodesCost
08816946
122116222
280015522
3362215482
done500115457

prune397.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.re y.re (* y.im y.im)))) (sqrt (fma y.re y.re (* y.im y.im))))
14.8b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.re y.re (* y.im y.im))))
27.1b
(sqrt (fma y.re y.re (* y.im y.im)))
27.1b
(sqrt (fma y.re y.re (* y.im y.im)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 fma-udef hypot-def
1×flip3-- flip--
Counts
4 → 254
Calls
4 calls:
25.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.re y.re (* y.im y.im)))) (sqrt (fma y.re y.re (* y.im y.im))))
26.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.re y.re (* y.im y.im))))
2.0ms
(sqrt (fma y.re y.re (* y.im y.im)))
2.0ms
(sqrt (fma y.re y.re (* y.im y.im)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.re y.re (* y.im y.im)))) (sqrt (fma y.re y.re (* y.im y.im))))
160.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.re y.re (* y.im y.im))))
64.0ms
(sqrt (fma y.re y.re (* y.im y.im)))
57.0ms
(sqrt (fma y.re y.re (* y.im y.im)))

simplify1.8s

Counts
266 → 266
Iterations

Useful iterations: done (1.7s)

IterNodesCost
0273163498
1678152978
23354129777
done5000129697

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.9b

localize53.0ms

Local error

Found 4 expressions with local error:

14.4b
(/ (/ (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) 1) (* (hypot y.re y.im) (/ (hypot y.re y.im) (cbrt (- (* x.im y.re) (* x.re y.im))))))
15.4b
(cbrt (- (* x.im y.re) (* x.re y.im)))
15.4b
(cbrt (- (* x.im y.re) (* x.re y.im)))
15.4b
(cbrt (- (* x.im y.re) (* x.re y.im)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log
32×div-exp
31×add-cbrt-cube
18×cbrt-undiv
16×prod-exp
13×times-frac
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×cbrt-prod cbrt-unprod
7×associate-/l*
6×cbrt-div 1-exp
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
3×flip3-- pow1/3 div-inv flip--
1×clear-num associate-/r* frac-2neg associate-*r/ associate-/r/ associate-/l/
Counts
4 → 98
Calls
4 calls:
35.0ms
(/ (/ (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) 1) (* (hypot y.re y.im) (/ (hypot y.re y.im) (cbrt (- (* x.im y.re) (* x.re y.im))))))
13.0ms
(cbrt (- (* x.im y.re) (* x.re y.im)))
7.0ms
(cbrt (- (* x.im y.re) (* x.re y.im)))
7.0ms
(cbrt (- (* x.im y.re) (* x.re y.im)))

series716.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (/ (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) 1) (* (hypot y.re y.im) (/ (hypot y.re y.im) (cbrt (- (* x.im y.re) (* x.re y.im))))))
181.0ms
(cbrt (- (* x.im y.re) (* x.re y.im)))
175.0ms
(cbrt (- (* x.im y.re) (* x.re y.im)))
187.0ms
(cbrt (- (* x.im y.re) (* x.re y.im)))

simplify3.7s

Counts
110 → 110
Iterations

Useful iterations: done (3.7s)

IterNodesCost
017953161
156146503
2390644699
done500242992

prune932.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.5b

localize41.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
15.4b
(cbrt (- (* x.im y.re) (* x.re y.im)))
15.4b
(cbrt (- (* x.im y.re) (* x.re y.im)))
15.4b
(cbrt (- (* x.im y.re) (* x.re y.im)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
9×cbrt-prod add-sqr-sqrt *-un-lft-identity flip3-- add-exp-log add-cube-cbrt flip--
8×associate-/l/
7×add-cbrt-cube
4×expm1-log1p-u frac-times pow1 log1p-expm1-u add-log-exp
3×associate-/r* times-frac pow1/3
2×cbrt-undiv div-exp associate-*l/ associate-*r/
1×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
23.0ms
(/ (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
4.0ms
(cbrt (- (* x.im y.re) (* x.re y.im)))
5.0ms
(cbrt (- (* x.im y.re) (* x.re y.im)))
14.0ms
(cbrt (- (* x.im y.re) (* x.re y.im)))

series966.0ms

Counts
4 → 12
Calls
4 calls:
437.0ms
(/ (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
164.0ms
(cbrt (- (* x.im y.re) (* x.re y.im)))
169.0ms
(cbrt (- (* x.im y.re) (* x.re y.im)))
196.0ms
(cbrt (- (* x.im y.re) (* x.re y.im)))

simplify2.0s

Counts
88 → 88
Iterations

Useful iterations: done (2.0s)

IterNodesCost
014435389
138233011
2149932771
done500131904

prune673.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 13.5b

regimes726.0ms

Accuracy

0% (3.4b remaining)

Error of 17.6b against oracle of 14.2b and baseline of 17.6b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
013419
115419
done15419

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.2s8438×body80valid