Details

simplify38.0m (85.5%)

sample3.3m (7.4%)

Algorithm
67×halfpoints

prune2.2m (4.9%)

localize33.8s (1.3%)

regimes18.6s (0.7%)

Accuracy

Total 7.9b remaining (31.6%)

Threshold costs 7.9b (31.6%)

0.9b0%Octave 3.8, jcobi/4
0.5b0%quadp (p42, positive)
0.4b0%quadm (p42, negative)
0.4b0%math.sqrt on complex, imaginary part, im greater than 0 branch
0.4b0%_divideComplex, imaginary part

rewrite5.7s (0.2%)

Algorithm
123×rewrite-expression-head
Calls

400 calls:

478.0ms
(/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))))
267.0ms
(+.p16 (/.p16 (/.p16 (*.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0))) (real->posit16 1.0))
133.0ms
(/.p16 (/.p16 (*.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
118.0ms
(/.p16 (/.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
112.0ms
(/.p16 (*.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 alpha (+.p16 beta i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
Rules
4564×p16-times-frac
4478×*p16-lft-identity-expand p16-*-un-lft-identity
3512×*p16-rgt-identity-expand
1077×/p16-rgt-identity-expand
961×introduce-quire
853×+p16-lft-identity-expand +p16-rgt-identity-expand
713×distribute-lft-out p16-distribute-lft-out
630×-p16-rgt-identity-expand
546×distribute-lft-in distribute-rgt-in
528×associate-/r*
510×distribute-lft-out--
504×associate-/r/
455×associate-/l*
406×associate-*l*
396×associate-*r*
350×associate--l+
347×insert-quire-fdp-add
317×distribute-rgt-out
216×insert-quire-fdp-sub
209×distribute-rgt-out--
203×associate-*r/
183×associate-*l/
172×p16-flip--
159×difference-of-squares
151×associate-/l/
144×associate-+l+
140×associate-+r+
122×associate--r+
104×sub-neg insert-quire-add
97×insert-quire-sub
88×*-commutative
84×associate-+l-
71×associate-+r- associate--r-
69×associate--l-
67×+-commutative
53×distribute-lft1-in
23×difference-of-sqr-1
remove-double-div.p16
sqrt-sqrd.p16

series29.0ms (0.0%)

Calls

400 calls:

0.0ms
(-.p16 (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 c a))) b_2)
0.0ms
(-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
0.0ms
(-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (*.p16 c a) (real->posit16 4)))) b)
0.0ms
(*.p16 (-.p16 re im) (+.p16 im re))
0.0ms
(-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))

bsearch1.0ms (0.0%)

end1.0ms (0.0%)