Details

simplify15.8m (71.2%)

sample3.2m (14.6%)

Algorithm
69×halfpoints

prune2.2m (9.7%)

localize32.8s (2.5%)

regimes18.9s (1.4%)

Accuracy

Total 8.3b remaining (32.9%)

Threshold costs 8.3b (32.9%)

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

rewrite7.7s (0.6%)

Algorithm
123×rewrite-expression-head
Calls

400 calls:

510.0ms
(/.p16 (+.p16 (real->posit16 1) (+.p16 (*.p16 (*.p16 x x) (+.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (real->posit16 0.0072644182)) (+.p16 (real->posit16 0.1049934947) (*.p16 (*.p16 x x) (real->posit16 0.0424060604))))) (+.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 (*.p16 x x) (*.p16 x x))) (*.p16 (*.p16 x x) (real->posit16 0.0001789971))) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 (*.p16 x x) (*.p16 x x))) (real->posit16 0.0005064034))))) (+.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (+.p16 (real->posit16 0.2909738639) (*.p16 (*.p16 x x) (real->posit16 0.0694555761)))) (+.p16 (+.p16 (real->posit16 1) (*.p16 (*.p16 x x) (real->posit16 0.7715471019))) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 (*.p16 x x) (*.p16 x x))) (+.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (real->posit16 2)) (real->posit16 0.0001789971)) (+.p16 (*.p16 x (*.p16 x (real->posit16 0.0008327945))) (real->posit16 0.0140005442)))))))
497.0ms
(-.p16 (/.p16 (+.p16 (+.p16 a b) c) (real->posit16 2)) a)
466.0ms
(/.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)))
202.0ms
(+.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))
188.0ms
(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) alpha) beta)) (real->posit16 1.0)) (real->posit16 2.0))
Rules
13086×p16-times-frac
10513×*p16-lft-identity-expand p16-*-un-lft-identity
6300×*p16-rgt-identity-expand
2000×distribute-lft-out--
1661×distribute-lft-out p16-distribute-lft-out
1546×/p16-rgt-identity-expand
947×associate-/r/
922×introduce-quire
764×distribute-rgt-out--
738×+p16-lft-identity-expand +p16-rgt-identity-expand
701×distribute-rgt-out
613×-p16-rgt-identity-expand
575×associate-/l*
561×associate-*r*
551×associate-/r*
349×associate-*l*
290×insert-quire-fdp-add
276×associate-*l/
228×insert-quire-fdp-sub
227×distribute-lft-in distribute-rgt-in
207×associate--l+
189×associate-*r/
179×p16-flip--
156×associate-/l/
140×associate-+r+
138×associate-+l+
124×associate--r+
105×sub-neg
103×insert-quire-sub
91×insert-quire-add
82×*-commutative
78×difference-of-squares
77×associate-+l-
73×associate--l-
67×associate-+r- distribute-lft1-in
63×+-commutative
60×associate--r-
19×difference-of-sqr-1
sqrt-sqrd.p16 remove-double-div.p16

series30.0ms (0.0%)

Calls

400 calls:

0.0ms
(-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
0.0ms
(-.p16 (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 c a))) b_2)
0.0ms
(-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (*.p16 c a) (real->posit16 4)))) b)
0.0ms
(-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
0.0ms
(/.p16 (+.p16 (real->posit16 1) (+.p16 (*.p16 (*.p16 x x) (+.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (real->posit16 0.0072644182)) (+.p16 (real->posit16 0.1049934947) (*.p16 (*.p16 x x) (real->posit16 0.0424060604))))) (+.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 (*.p16 x x) (*.p16 x x))) (*.p16 (*.p16 x x) (real->posit16 0.0001789971))) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 (*.p16 x x) (*.p16 x x))) (real->posit16 0.0005064034))))) (+.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (+.p16 (real->posit16 0.2909738639) (*.p16 (*.p16 x x) (real->posit16 0.0694555761)))) (+.p16 (+.p16 (real->posit16 1) (*.p16 (*.p16 x x) (real->posit16 0.7715471019))) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 (*.p16 x x) (*.p16 x x))) (+.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (real->posit16 2)) (real->posit16 0.0001789971)) (+.p16 (*.p16 x (*.p16 x (real->posit16 0.0008327945))) (real->posit16 0.0140005442)))))))

bsearch1.0ms (0.0%)

end1.0ms (0.0%)