Details

sample3.7m

Algorithm

66×	halfpoints

Results

simplify1.9m

Calls

746 calls:

Slowest

1.4s	(.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 (/.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 (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))
1.3s	(/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))
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)))

prune1.5m

regimes33.3s

Accuracy

Total -1769.0b remaining (-6538.2%)

-60.8b	-∞%	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

rewrite29.8s

Algorithm

111×	rewrite-expression-head

Calls

375 calls:

Slowest

7.5s	(/.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)))))
6.7s	(/.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))))
6.7s	(/.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))))
6.6s	(/.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 (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))))
84.0ms	(+.p16 (.p16 im re) (.p16 im re))

Rules

133×	`p16-flip--`
99×	`sub-neg`
95×	`*-commutative`
93×	`+-commutative`
54×	`distribute-lft-in` `distribute-rgt-in`
52×	`associate-/l/`
36×	`associate-*l/`
35×	`associate-*r/`
34×	`associate-/r/`
29×	`associate-+l+` `associate-/l` `associate-r*`
27×	`associate-+r+`
24×	`difference-of-squares` `associate-/r*`
20×	`associate-l`
15×	`distribute-lft-out` `p16-distribute-lft-out`
12×	`p16-times-frac`
10×	`associate--l+`
8×	`difference-of-sqr-1` `associate-+l-`
5×	`associate-+r-`
4×	`sqrt-sqrd.p16` `distribute-rgt-out`
3×	`associate--r-`
1×	`associate--l-` `associate--r+`

localize29.0s

bsearch137.0ms

series29.0ms

Calls

375 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 (neg.p16 b_2) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 a c))))
0.0ms	(*.p16 (-.p16 re im) (+.p16 im re))

Details

sample3.7m

simplify1.9m

prune1.5m

regimes33.3s

rewrite29.8s

localize29.0s

bsearch137.0ms

series29.0ms

end1.0ms