Details

Time bar (total: 30.0s)

sample35.0ms

Algorithm
intervals
Results
25.0ms273×body80valid

simplify30.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
30.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize20.0ms

Local error

Found 3 expressions with local error:

24.1b
(/ (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
Counts
3 → 52
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))

series220.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
126.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
57.0ms
(fma x.re y.re (* x.im y.im))
37.0ms
(fma y.im y.im (* y.re y.re))

simplify1.2s

Counts
34 → 61
Calls
34 calls:
Slowest
414.0ms
(/ (* (* (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))))
62.0ms
(/ (* (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)))))
48.0ms
(- (log (fma x.re y.re (* x.im y.im))) (log (fma y.im y.im (* y.re y.re))))
41.0ms
(/ (* (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))))
38.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

prune772.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.7b

localize27.0ms

Local error

Found 4 expressions with local error:

29.3b
(sqrt (fma y.im y.im (* y.re y.re)))
29.3b
(sqrt (fma y.im y.im (* y.re y.re)))
13.3b
(/ (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))

rewrite16.0ms

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 add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 87
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))

series310.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
149.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
62.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
59.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
41.0ms
(fma x.re y.re (* x.im y.im))

simplify1.9s

Counts
68 → 99
Calls
68 calls:
Slowest
240.0ms
(/ (* (* (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)))))
74.0ms
(/ (* (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))))))
67.0ms
(/ (* (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)))))
58.0ms
(/ (* (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)))))
51.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.6b

localize49.0ms

Local error

Found 4 expressions with local error:

29.3b
(sqrt (fma y.im y.im (* y.re y.re)))
13.3b
(/ (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))
0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
96×add-sqr-sqrt
95×*-un-lft-identity add-cube-cbrt
51×sqrt-prod
25×associate-/l*
11×add-cbrt-cube add-exp-log
9×associate-/r*
6×div-inv
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg fma-udef
1×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def associate-/l/
Counts
4 → 179
Calls
4 calls:
Slowest
17.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
17.0ms
(/ (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)))
0.0ms
(fma x.re y.re (* x.im y.im))

series519.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
221.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
187.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
62.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
49.0ms
(fma x.re y.re (* x.im y.im))

simplify11.2s

Counts
224 → 191
Calls
224 calls:
Slowest
309.0ms
(/ (* (* (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)))))
303.0ms
(/ (/ (* (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)))))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))
235.0ms
(/ (/ (* (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)))))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))
200.0ms
(/ (/ (* (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)))))) (sqrt (hypot y.im y.re)))
185.0ms
(/ (/ (* (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))))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))

prune2.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.9b

localize32.0ms

Local error

Found 3 expressions with local error:

13.3b
(/ (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))

rewrite14.0ms

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/
Counts
3 → 114
Calls
3 calls:
Slowest
8.0ms
(/ (/ (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))

series372.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
154.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
143.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
74.0ms
(fma x.re y.re (* x.im y.im))

simplify5.5s

Counts
132 → 123
Calls
132 calls:
Slowest
481.0ms
(/ (* (* (/ (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)))
241.0ms
(/ (* (* (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)))
194.0ms
(/ (/ (* (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))))
192.0ms
(/ (/ (* (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))))
157.0ms
(/ (/ (* (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)))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.9b

regimes355.0ms

Accuracy

33.7% (6.9b remaining)

Error of 12.5b against oracle of 5.6b and baseline of 16.1b

bsearch106.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.6s8470×body80valid