Details

Time bar (total: 28.0s)

sample49.0ms

Algorithm
intervals
Results
36.0ms274×body80valid

simplify14.0ms

Calls
1 calls:
Slowest
13.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize48.0ms

Local error

Found 2 expressions with local error:

27.0b
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.5b
(fma x.re y.re (* x.im y.im))

rewrite8.0ms

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
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Calls
2 calls:
Slowest
7.0ms
(/ (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))

series91.0ms

Calls
2 calls:
Slowest
60.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
31.0ms
(fma x.re y.re (* x.im y.im))

simplify1.2s

Calls
31 calls:
Slowest
408.0ms
(/ (* (* (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))))
72.0ms
(/ (* (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)))))
50.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (fma y.im y.im (* y.re y.re))))
47.0ms
(- (log (fma x.re y.re (* x.im y.im))) (log (fma y.im y.im (* y.re y.re))))
44.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) 1)

prune583.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 26.5b

localize16.0ms

Local error

Found 4 expressions with local error:

28.3b
(sqrt (fma y.im y.im (* y.re y.re)))
28.3b
(sqrt (fma y.im y.im (* y.re y.re)))
18.5b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.5b
(fma x.re y.re (* x.im y.im))

rewrite15.0ms

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
9.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
0.0ms
(fma x.re y.re (* x.im y.im))

series214.0ms

Calls
4 calls:
Slowest
96.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
45.0ms
(fma x.re y.re (* x.im y.im))
42.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
31.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.9s

Calls
66 calls:
Slowest
331.0ms
(/ (* (* (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)))))
96.0ms
(/ (* (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))))))
57.0ms
(/ (* (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)))))
50.0ms
(/ (sqrt (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))))))
46.0ms
(- (log (fma x.re y.re (* x.im y.im))) (log (sqrt (fma y.im y.im (* y.re y.re)))))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 23.8b

localize18.0ms

Local error

Found 4 expressions with local error:

28.3b
(sqrt (fma y.im y.im (* y.re y.re)))
18.5b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
0.5b
(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))))

rewrite32.0ms

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
18.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
9.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
0.0ms
(fma x.re y.re (* x.im y.im))

series313.0ms

Calls
4 calls:
Slowest
162.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
104.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
26.0ms
(fma x.re y.re (* x.im y.im))
22.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify10.3s

Calls
220 calls:
Slowest
426.0ms
(/ (* (* (/ (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)))))
266.0ms
(/ (/ (* (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 (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))
197.0ms
(/ (* (* (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)))
191.0ms
(/ (/ (* (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)))))
176.0ms
(/ (/ (* (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)))))

prune2.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.1b

localize3.0ms

Local error

Found 3 expressions with local error:

18.5b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
0.5b
(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))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
10×add-cbrt-cube add-exp-log
6×associate-/r* div-inv
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×fma-udef associate-/l/
Calls
3 calls:
Slowest
10.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
4.0ms
(/ (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))

series249.0ms

Calls
3 calls:
Slowest
112.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
109.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
27.0ms
(fma x.re y.re (* x.im y.im))

simplify5.0s

Calls
132 calls:
Slowest
482.0ms
(/ (* (* (/ (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)))
263.0ms
(/ (* (* (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)))
173.0ms
(/ (/ (* (* (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))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
138.0ms
(/ (/ (* (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))))
132.0ms
(/ (/ (* (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)))

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.0b

regimes466.0ms

Accuracy

35% (6.8b remaining)

Error of 12.7b against oracle of 5.9b and baseline of 16.4b

bsearch190.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.2s8482×body80valid