Details

Time bar (total: 28.5s)

sample34.0ms

Algorithm
intervals
Results
24.0ms269×body80valid

simplify16.0ms

Calls
1 calls:
Slowest
16.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize29.0ms

Local error

Found 3 expressions with local error:

25.2b
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.3b
(fma x.re y.re (* x.im y.im))
0.0b
(fma y.im y.im (* y.re y.re))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×fma-udef
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Calls
3 calls:
Slowest
4.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.0ms
(fma x.re y.re (* x.im y.im))
0.0ms
(fma y.im y.im (* y.re y.re))

series129.0ms

Calls
3 calls:
Slowest
66.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
35.0ms
(fma x.re y.re (* x.im y.im))
28.0ms
(fma y.im y.im (* y.re y.re))

simplify1.1s

Calls
34 calls:
Slowest
348.0ms
(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re))))
78.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re)))))
46.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) 1)
45.0ms
(/ (sqrt (fma x.re y.re (* x.im y.im))) (cbrt (fma y.im y.im (* y.re y.re))))
43.0ms
(/ (sqrt (fma x.re y.re (* x.im y.im))) (sqrt (fma y.im y.im (* y.re y.re))))

prune618.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.8b

localize9.0ms

Local error

Found 4 expressions with local error:

29.5b
(sqrt (fma y.im y.im (* y.re y.re)))
29.5b
(sqrt (fma y.im y.im (* y.re y.re)))
15.9b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.3b
(fma x.re y.re (* x.im y.im))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef associate-/l*
2×rem-sqrt-square pow1/2 hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Calls
4 calls:
Slowest
4.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
0.0ms
(fma x.re y.re (* x.im y.im))

series220.0ms

Calls
4 calls:
Slowest
98.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
46.0ms
(fma x.re y.re (* x.im y.im))
43.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
33.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.0s

Calls
66 calls:
Slowest
282.0ms
(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (sqrt (fma y.im y.im (* y.re y.re))) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re)))))
71.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))
60.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt 1))
56.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re))))))
54.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.0b

localize9.0ms

Local error

Found 4 expressions with local error:

29.5b
(sqrt (fma y.im y.im (* y.re y.re)))
15.9b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
0.3b
(fma x.re y.re (* x.im y.im))
0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
91×add-sqr-sqrt
90×*-un-lft-identity add-cube-cbrt
45×sqrt-prod
16×associate-/l*
11×add-cbrt-cube add-exp-log
9×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg fma-udef
1×rem-sqrt-square pow1/2 hypot-def associate-/l/
Calls
4 calls:
Slowest
16.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
7.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
0.0ms
(fma x.re y.re (* x.im y.im))

series321.0ms

Calls
4 calls:
Slowest
137.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
117.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
44.0ms
(fma x.re y.re (* x.im y.im))
22.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify11.1s

Calls
220 calls:
Slowest
490.0ms
(/ (* (* (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))) (* (* (sqrt (fma y.im y.im (* y.re y.re))) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re)))))
424.0ms
(/ (/ (sqrt (fma x.re y.re (* x.im y.im))) (sqrt (hypot y.im y.re))) (sqrt (cbrt (fma y.im y.im (* y.re y.re)))))
291.0ms
(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
227.0ms
(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re)))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
220.0ms
(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re)))) (sqrt (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re))))))

prune2.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.5b

localize4.0ms

Local error

Found 4 expressions with local error:

15.9b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
0.3b
(fma x.re y.re (* x.im y.im))
0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.0b
(hypot y.im y.re)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
11×add-cbrt-cube add-exp-log
6×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×hypot-udef fma-udef associate-/l/
Calls
4 calls:
Slowest
10.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
8.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
0.0ms
(fma x.re y.re (* x.im y.im))
0.0ms
(hypot y.im y.re)

series267.0ms

Calls
4 calls:
Slowest
106.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
103.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
33.0ms
(fma x.re y.re (* x.im y.im))
26.0ms
(hypot y.im y.re)

simplify5.0s

Calls
135 calls:
Slowest
402.0ms
(/ (* (* (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
280.0ms
(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
158.0ms
(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re)))) (sqrt (hypot y.im y.re)))
147.0ms
(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (hypot y.im y.re))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))
145.0ms
(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

regimes421.0ms

Accuracy

34.1% (7.0b remaining)

Error of 12.7b against oracle of 5.7b and baseline of 16.3b

bsearch135.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.3s8484×body80valid