Details

sample3.3m

Algorithm

66×	halfpoints

Results

simplify1.6m

Calls

752 calls:

Slowest

1.4s	(.p16 (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) (-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (*.p16 b_2 b_2)))
1.2s	(-.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)))))))
1.1s	(.p16 (real->posit16 0.5) (sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re))))
1.1s	(-.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 (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)))

prune1.4m

regimes29.8s

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

localize24.8s

rewrite24.0s

Algorithm

111×	rewrite-expression-head

Calls

375 calls:

Slowest

5.7s	(/.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 (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))))
5.5s	(/.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 (.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))))
5.5s	(/.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)))))
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 (.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))))
32.0ms	(+.p16 (+.p16 (+.p16 (real->posit16 5) d3) d2) (real->posit16 32))

Rules

136×	`p16-flip--`
104×	`sub-neg`
95×	`*-commutative`
91×	`+-commutative`
55×	`distribute-lft-in` `distribute-rgt-in`
52×	`associate-/l/`
36×	`associate-r/` `associate-l/`
34×	`associate-/r/`
29×	`associate-+l+` `associate-/l` `associate-r*`
25×	`associate-/r*` `associate-+r+`
24×	`difference-of-squares`
20×	`associate-l`
17×	`distribute-lft-out` `p16-distribute-lft-out`
12×	`p16-times-frac`
10×	`associate--l+`
8×	`difference-of-sqr-1` `associate--r-` `associate-+l-`
4×	`sqrt-sqrd.p16` `associate--r+`
2×	`associate-+r-` `distribute-rgt-out`
1×	`associate--l-`

bsearch114.0ms

series24.0ms

Calls

375 calls:

Slowest

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 (.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 (+.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)))))

end1.0ms