Details

sample3.3m

Algorithm

66×	halfpoints

Results

simplify1.7m

Calls

747 calls:

Slowest

1.4s	(-.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)))))))
1.3s	(-.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)))))))
1.2s	(-.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)))
1.2s	(-.p16 (.p16 (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))) (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a))))) (.p16 b_2 b_2))
1.2s	(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))

prune1.3m

regimes27.6s

Accuracy

Total -1768.7b remaining (-6469.3%)

-60.5b	-∞%	Jmat.Real.dawson
-61.7b	-∞%	quad2p (problem 3.2.1, positive)
-61.8b	-∞%	quadp (p42, positive)
-62.0b	-∞%	math.sqrt on complex, imaginary part, im greater than 0 branch
-62.5b	-∞%	Octave 3.8, jcobi/4

rewrite27.4s

Algorithm

112×	rewrite-expression-head

Calls

377 calls:

Slowest

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 (real->posit16 0.0005064034) (.p16 (.p16 (.p16 (.p16 x x) (.p16 x x)) (.p16 x x)) (.p16 x x)))) (.p16 (.p16 (real->posit16 0.0001789971) (.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 (.p16 (real->posit16 2) (real->posit16 0.0001789971)) (.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)))))
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 (.p16 (.p16 (real->posit16 2) (real->posit16 0.0001789971)) (.p16 (.p16 (.p16 (.p16 x x) (.p16 x x)) (.p16 x x)) (.p16 x x))) (.p16 x x)) (*.p16 x x))))
6.0s	(/.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))))
60.0ms	(*.p16 (+.p16 (+.p16 (+.p16 (real->posit16 5) d3) d2) (real->posit16 32)) d1)

Rules

140×	`p16-flip--`
114×	`sub-neg`
94×	`+-commutative`
88×	`*-commutative`
68×	`distribute-lft-in` `distribute-rgt-in`
59×	`associate-/l/`
42×	`associate-*r/`
39×	`associate-/r/`
33×	`associate-+l+`
32×	`associate-r`
30×	`associate-*l/`
28×	`associate-/l*`
23×	`associate-+r+`
21×	`difference-of-squares` `associate-/r*`
20×	`associate--l+`
19×	`associate-l`
17×	`distribute-lft-out` `p16-distribute-lft-out`
8×	`difference-of-sqr-1` `associate-+l-` `p16-times-frac`
4×	`associate--r-`
3×	`associate--l-` `sqrt-sqrd.p16`
1×	`distribute-lft-out--` `associate-+r-` `associate--r+` `distribute-rgt-out`

localize25.5s

bsearch117.0ms

series26.0ms

Calls

377 calls:

Slowest

1.0ms	(/.p16 (+.p16 (+.p16 alpha beta) (+.p16 (.p16 beta alpha) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))
0.0ms	(/.p16 (-.p16 (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))) b_2) a)
0.0ms	(+.p16 (.p16 y.re y.re) (.p16 y.im y.im))
0.0ms	(-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 a c))))
0.0ms	(-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c)))))

Details

sample3.3m

simplify1.7m

prune1.3m

regimes27.6s

rewrite27.4s

localize25.5s

bsearch117.0ms

series26.0ms

end1.0ms