Details

sample3.3m

Algorithm

66×	halfpoints

Results

simplify1.6m

Calls

787 calls:

Slowest

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)))))))
1.3s	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
1.1s	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
1.0s	(.p16 alpha (/.p16 (-.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha))))
1.0s	(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))

prune1.4m

regimes28.8s

Accuracy

Total -1768.8b remaining (-6469.3%)

-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

localize25.7s

rewrite24.6s

Algorithm

112×	rewrite-expression-head

Calls

376 calls:

Slowest

5.9s	(/.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)))))
5.6s	(/.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))))
5.4s	(/.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 (.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 (.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))))
422.0ms	(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 a c)))) a)

Rules

136×	`p16-flip--`
113×	`sub-neg`
97×	`*-commutative`
91×	`+-commutative`
79×	`distribute-lft-in` `distribute-rgt-in`
58×	`associate-/l/`
37×	`associate-/l*`
36×	`associate-*r/`
34×	`associate-r`
32×	`associate-*l/`
28×	`associate-/r*`
25×	`difference-of-squares` `associate--l+`
23×	`associate-+l+` `associate-/r/`
22×	`associate-+r+` `p16-times-frac`
19×	`distribute-lft-out` `associate-l` `p16-distribute-lft-out`
11×	`difference-of-sqr-1` `associate--r+`
6×	`associate-+l-`
5×	`associate--r-`
4×	`distribute-rgt-out`
3×	`sqrt-sqrd.p16`
2×	`associate--l-`
1×	`associate-+r-`

bsearch107.0ms

series26.0ms

Calls

376 calls:

Slowest

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

Details

sample3.3m

simplify1.6m

prune1.4m

regimes28.8s

localize25.7s

rewrite24.6s

bsearch107.0ms

series26.0ms

end1.0ms