Details

sample3.3m

Algorithm
66×halfpoints
Results

simplify1.7m

Calls

823 calls:

Slowest
1.2s
(-.p16 (*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))) (*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))))
1.1s
(*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand) (neg.p16 (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
1.1s
(/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))
1.1s
(/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))
1.1s
(-.p16 (*.p16 (/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 x))) (sqrt.p16 x)) (/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 x))) (sqrt.p16 x))) (*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))))

prune1.4m

regimes27.7s

Accuracy

Total -1768.8b remaining (-6475.1%)

-60.7b-∞%Jmat.Real.dawson
-61.7b-∞%quad2p (problem 3.2.1, positive)
-61.8b-∞%quadp (p42, positive)
-61.9b-∞%math.sqrt on complex, imaginary part, im greater than 0 branch
-62.5b-∞%Octave 3.8, jcobi/4

rewrite24.6s

Algorithm
112×rewrite-expression-head
Calls

376 calls:

Slowest
6.2s
(/.p16 (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (real->posit16 1) (*.p16 (real->posit16 0.1049934947) (*.p16 x x))) (*.p16 (real->posit16 0.0424060604) (*.p16 (*.p16 x x) (*.p16 x x)))) (*.p16 (real->posit16 0.0072644182) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0005064034) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0001789971) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (real->posit16 1) (*.p16 (real->posit16 0.7715471019) (*.p16 x x))) (*.p16 (real->posit16 0.2909738639) (*.p16 (*.p16 x x) (*.p16 x x)))) (*.p16 (real->posit16 0.0694555761) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0140005442) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0008327945) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (*.p16 (*.p16 (real->posit16 2) (real->posit16 0.0001789971)) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x))) (*.p16 x x))))
6.1s
(/.p16 (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (real->posit16 1) (*.p16 (real->posit16 0.1049934947) (*.p16 x x))) (*.p16 (real->posit16 0.0424060604) (*.p16 (*.p16 x x) (*.p16 x x)))) (*.p16 (real->posit16 0.0072644182) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)))) (*.p16 (*.p16 (real->posit16 0.0005064034) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x))) (*.p16 x x))) (*.p16 (real->posit16 0.0001789971) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (real->posit16 1) (*.p16 (real->posit16 0.7715471019) (*.p16 x x))) (*.p16 (real->posit16 0.2909738639) (*.p16 (*.p16 x x) (*.p16 x x)))) (*.p16 (real->posit16 0.0694555761) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0140005442) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (*.p16 (real->posit16 0.0008327945) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x))) (*.p16 x x))) (*.p16 (*.p16 (*.p16 (real->posit16 2) (real->posit16 0.0001789971)) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x))) (*.p16 x x))))
5.3s
(/.p16 (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (real->posit16 1) (*.p16 (real->posit16 0.1049934947) (*.p16 x x))) (*.p16 (real->posit16 0.0424060604) (*.p16 (*.p16 x x) (*.p16 x x)))) (*.p16 (real->posit16 0.0072644182) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0005064034) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0001789971) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (real->posit16 1) (*.p16 (real->posit16 0.7715471019) (*.p16 x x))) (*.p16 (real->posit16 0.2909738639) (*.p16 (*.p16 x x) (*.p16 x x)))) (*.p16 (real->posit16 0.0694555761) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0140005442) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0008327945) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (*.p16 (real->posit16 2) (real->posit16 0.0001789971)) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))))
5.0s
(/.p16 (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (real->posit16 1) (*.p16 (real->posit16 0.1049934947) (*.p16 x x))) (*.p16 (real->posit16 0.0424060604) (*.p16 (*.p16 x x) (*.p16 x x)))) (*.p16 (real->posit16 0.0072644182) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0005064034) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0001789971) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (real->posit16 1) (*.p16 (real->posit16 0.7715471019) (*.p16 x x))) (*.p16 (real->posit16 0.2909738639) (*.p16 (*.p16 x x) (*.p16 x x)))) (*.p16 (real->posit16 0.0694555761) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0140005442) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (*.p16 (real->posit16 0.0008327945) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x))) (*.p16 x x))) (*.p16 (*.p16 (*.p16 (real->posit16 2) (real->posit16 0.0001789971)) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x))) (*.p16 x x))))
45.0ms
(+.p16 (+.p16 (+.p16 (real->posit16 5) d3) d2) (real->posit16 32))
Rules
134×p16-flip--
131×sub-neg
97×*-commutative
93×distribute-lft-in distribute-rgt-in
92×+-commutative
58×associate-/l/
38×associate-/l*
37×associate-*r/
34×associate-*r*
33×associate-*l/
31×associate-+r+
28×associate-/r* associate--l+
27×associate-+l+
25×difference-of-squares
24×p16-times-frac
23×associate-/r/
21×associate-*l*
19×distribute-lft-out p16-distribute-lft-out
11×difference-of-sqr-1
9×associate--r+
6×associate-+l-
5×distribute-rgt-out
4×associate-+r- associate--r-
3×associate--l- sqrt-sqrd.p16

localize24.3s

bsearch120.0ms

series28.0ms

Calls

376 calls:

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

end1.0ms