Details

prune11.6m (53.0%)

simplify5.8m (26.6%)

sample3.3m (15.3%)

Algorithm
69×halfpoints

localize36.7s (2.8%)

regimes20.7s (1.6%)

Accuracy

Total 8.7b remaining (33.7%)

Threshold costs 8.7b (33.7%)

0.9b0%Octave 3.8, jcobi/4
0.5b0%quadm (p42, negative)
0.4b0%math.sqrt on complex, imaginary part, im greater than 0 branch
0.4b0%quadp (p42, positive)
0.4b0%quad2p (problem 3.2.1, positive)

rewrite7.7s (0.6%)

Algorithm
123×rewrite-expression-head
Calls

401 calls:

527.0ms
(/.p16 (/.p16 (+.p16 (*.p16 beta alpha) (*.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)))
455.0ms
(/.p16 (+.p16 (+.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 (*.p16 x x) (*.p16 x x))) (+.p16 (real->posit16 0.0005064034) (*.p16 (*.p16 x x) (real->posit16 0.0001789971)))) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (+.p16 (*.p16 (real->posit16 0.0072644182) (*.p16 x x)) (real->posit16 0.0424060604)))) (+.p16 (real->posit16 1) (*.p16 (*.p16 x x) (real->posit16 0.1049934947)))) (+.p16 (*.p16 (*.p16 x x) (+.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (+.p16 (real->posit16 0.0694555761) (*.p16 (real->posit16 0.0140005442) (*.p16 x x)))) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 (*.p16 x x) (*.p16 x x))) (+.p16 (real->posit16 0.0008327945) (*.p16 (real->posit16 2) (*.p16 (*.p16 x x) (real->posit16 0.0001789971))))))) (+.p16 (real->posit16 1) (*.p16 (*.p16 x x) (+.p16 (real->posit16 0.7715471019) (*.p16 (*.p16 x x) (real->posit16 0.2909738639)))))))
222.0ms
(/.p16 (-.p16 (/.p16 (+.p16 (+.p16 a b) c) (real->posit16 2)) b) (+.p16 (/.p16 (+.p16 (+.p16 a b) c) (real->posit16 2)) b))
178.0ms
(/.p16 (+.p16 (/.p16 (+.p16 (+.p16 a b) c) (real->posit16 2)) b) (-.p16 (/.p16 (+.p16 (+.p16 a b) c) (real->posit16 2)) b))
151.0ms
(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
Rules
9036×p16-times-frac
7471×*p16-lft-identity-expand p16-*-un-lft-identity
5820×*p16-rgt-identity-expand
1519×distribute-lft-out p16-distribute-lft-out
1129×/p16-rgt-identity-expand
957×introduce-quire
821×+p16-lft-identity-expand +p16-rgt-identity-expand
743×associate-/l*
706×associate-/r*
653×associate-*l*
641×-p16-rgt-identity-expand
636×distribute-rgt-out
589×associate-/r/
434×distribute-lft-in distribute-rgt-in
428×distribute-lft-out--
364×associate-*r*
330×insert-quire-fdp-add
260×associate--l+
214×insert-quire-fdp-sub
212×associate-*r/
202×associate-*l/
178×p16-flip--
166×distribute-rgt-out--
162×difference-of-squares associate-/l/
157×associate-+r+
149×associate-+l+
132×sub-neg
128×associate--r+
124×distribute-lft1-in
103×insert-quire-sub
95×insert-quire-add
83×associate-+r-
82×associate-+l-
75×*-commutative
71×+-commutative associate--r-
70×associate--l-
22×difference-of-sqr-1
distribute-rgt1-in
remove-double-div.p16

series61.0ms (0.0%)

Calls

401 calls:

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

end2.0ms (0.0%)

bsearch1.0ms (0.0%)