Details

Time bar (total: 12.9s)

sample33.0ms

Algorithm
intervals
Results
24.0ms260×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)))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.8b

localize16.0ms

Local error

Found 3 expressions with local error:

27.8b
(/ (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 y.im y.im (* y.re y.re))
0.0ms
(fma x.re y.re (* x.im y.im))

series137.0ms

Calls
3 calls:
Slowest
82.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
34.0ms
(fma x.re y.re (* x.im y.im))
20.0ms
(fma y.im y.im (* y.re y.re))

simplify1.1s

Calls
34 calls:
Slowest
398.0ms
(/ (* (* (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))))
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
(/ (* (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
(/ (sqrt (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)))))
45.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) 1)

prune674.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 27.4b

localize9.0ms

Local error

Found 4 expressions with local error:

33.3b
(sqrt (fma y.im y.im (* y.re y.re)))
33.3b
(sqrt (fma y.im y.im (* y.re y.re)))
16.2b
(/ (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×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
10.0ms
(/ (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))

series170.0ms

Calls
4 calls:
Slowest
93.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
27.0ms
(fma x.re y.re (* x.im y.im))
25.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
25.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.7s

Calls
66 calls:
Slowest
304.0ms
(/ (* (* (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)))))
57.0ms
(/ (* (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))))))
53.0ms
(- (log (fma x.re y.re (* x.im y.im))) (log (sqrt (fma y.im y.im (* y.re y.re)))))
49.0ms
(/ (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))))))
47.0ms
(/ (sqrt (fma x.re y.re (* x.im y.im))) (cbrt (sqrt (fma y.im y.im (* y.re y.re)))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.7b

localize23.0ms

Local error

Found 4 expressions with local error:

33.3b
(sqrt (fma y.im y.im (* y.re y.re)))
33.3b
(sqrt (fma y.im y.im (* y.re y.re)))
16.2b
(/ (fma y.im x.im (* y.re x.re)) (sqrt (fma y.im y.im (* y.re y.re))))
0.3b
(fma y.im x.im (* y.re x.re))

rewrite7.0ms

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 y.im x.im (* y.re x.re)) (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 y.im x.im (* y.re x.re))

series173.0ms

Calls
4 calls:
Slowest
73.0ms
(/ (fma y.im x.im (* y.re x.re)) (sqrt (fma y.im y.im (* y.re y.re))))
42.0ms
(fma y.im x.im (* y.re x.re))
34.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
23.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.8s

Calls
66 calls:
Slowest
276.0ms
(/ (* (* (fma y.im x.im (* y.re x.re)) (fma y.im x.im (* y.re x.re))) (fma y.im x.im (* y.re x.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)))))
56.0ms
(/ (* (cbrt (fma y.im x.im (* y.re x.re))) (cbrt (fma y.im x.im (* y.re x.re)))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
53.0ms
(/ (sqrt (fma y.im x.im (* y.re x.re))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
52.0ms
(/ (* (cbrt (fma y.im x.im (* y.re x.re))) (cbrt (fma y.im x.im (* y.re x.re)))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))
49.0ms
(/ (* (cbrt (fma y.im x.im (* y.re x.re))) (cbrt (fma y.im x.im (* y.re x.re)))) (sqrt (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re))))))

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.2b

localize9.0ms

Local error

Found 4 expressions with local error:

33.3b
(sqrt (fma y.im y.im (* y.re y.re)))
33.3b
(sqrt (fma y.im y.im (* y.re y.re)))
16.3b
(* (fma x.re y.re (* x.im y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
0.3b
(fma x.re y.re (* x.im y.im))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-exp-log add-cube-cbrt
6×pow1 add-cbrt-cube sqrt-prod
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* fma-udef
2×rem-sqrt-square pow1/2 prod-exp hypot-def
1×rec-exp pow-prod-down associate-*r/ un-div-inv *-commutative cbrt-unprod div-inv
Calls
4 calls:
Slowest
5.0ms
(* (fma x.re y.re (* x.im y.im)) (/ 1 (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))

series207.0ms

Calls
4 calls:
Slowest
103.0ms
(* (fma x.re y.re (* x.im y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
45.0ms
(fma x.re y.re (* x.im y.im))
36.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
22.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.2s

Calls
32 calls:
Slowest
600.0ms
(* (* (* (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))) (* (* (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))) (/ 1 (sqrt (fma y.im y.im (* y.re y.re))))) (/ 1 (sqrt (fma y.im y.im (* y.re y.re))))))
139.0ms
(* (fma x.re y.re (* x.im y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
104.0ms
(+ (log (fma x.re y.re (* x.im y.im))) (log (/ 1 (sqrt (fma y.im y.im (* y.re y.re))))))
33.0ms
(+ (log (fma x.re y.re (* x.im y.im))) (- (log (sqrt (fma y.im y.im (* y.re y.re))))))
32.0ms
(* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im))))

prune1.0s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 25.2b

regimes370.0ms

Accuracy

0% (2.6b remaining)

Error of 25.6b against oracle of 23.0b and baseline of 25.6b

bsearch2.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s8465×body80valid