Details

sample4.0m

Algorithm

66×	halfpoints

Results

simplify2.0m

Calls

732 calls:

Slowest

1.9s	(-.p16 (.p16 (neg.p16 b_2) (neg.p16 b_2)) (.p16 (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 a c) (.p16 a c))) (+.p16 (.p16 b_2 b_2) (.p16 a c)))) (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 a c) (.p16 a c))) (+.p16 (.p16 b_2 b_2) (.p16 a c))))))
1.6s	(.p16 (real->posit16 0.5) (sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re))))
1.4s	(-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0))
1.4s	(/.p16 (/.p16 i (/.p16 (.p16 (real->posit16 2) i) i)) (+.p16 (.p16 (real->posit16 2) i) (real->posit16 1.0)))
1.4s	(-.p16 (.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))))) (.p16 (.p16 re re) (.p16 re re)))

prune1.6m

regimes36.8s

Accuracy

Total -1769.1b remaining (-6557.4%)

-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

localize31.2s

rewrite29.4s

Algorithm

112×	rewrite-expression-head

Calls

376 calls:

Slowest

7.1s	(/.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 (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))))
7.0s	(/.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 (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))))
6.6s	(/.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))))
6.4s	(/.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)))))
65.0ms	(+.p16 (/.p16 (.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 beta alpha)) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0))) (real->posit16 1.0))

Rules

127×	`p16-flip--`
116×	`sub-neg`
101×	`+-commutative`
87×	`*-commutative`
57×	`distribute-lft-in` `distribute-rgt-in`
53×	`associate-/l/`
39×	`associate-/l*`
38×	`associate-/r/`
31×	`associate-+r+`
30×	`associate-r/` `associate-r*`
28×	`associate-+l+`
25×	`difference-of-squares`
22×	`associate-/r` `associate-l/` `p16-times-frac`
20×	`associate-l`
17×	`distribute-lft-out` `p16-distribute-lft-out`
14×	`associate--l+`
9×	`difference-of-sqr-1`
6×	`associate-+r-` `associate-+l-`
4×	`distribute-rgt-out`
3×	`sqrt-sqrd.p16`
1×	`associate--l-` `associate--r+` `associate--r-`

bsearch162.0ms

series32.0ms

Calls

376 calls:

Slowest

0.0ms	(.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
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 (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)

Details

sample4.0m

simplify2.0m

prune1.6m

regimes36.8s

localize31.2s

rewrite29.4s

bsearch162.0ms

series32.0ms

end2.0ms