Details

sample196.0ms

Algorithm

halfpoints

Results

simplify858.0ms

Calls

1 calls:

Slowest

858.0ms

(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune42.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize379.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.3b	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b	(/.p16 (real->posit16 1) (sqrt.p16 x))
0.1b	(sqrt.p16 (+.p16 x (real->posit16 1)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

1×	`sub-neg` `p16-flip--`

Calls

4 calls:

Slowest

6.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
3.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
3.0ms	(/.p16 (real->posit16 1) (sqrt.p16 x))
0.0ms	(sqrt.p16 (+.p16 x (real->posit16 1)))

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms	(/.p16 (real->posit16 1) (sqrt.p16 x))
0.0ms	(sqrt.p16 (+.p16 x (real->posit16 1)))

simplify3.7s

Calls

4 calls:

Slowest

1.1s	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
996.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
854.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
827.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune199.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.9b

localize178.0ms

Local error

Found 4 expressions with local error:

0.7b	(-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.5b	(/.p16 (-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (.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 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.4b	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))
0.3b	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
8×	`difference-of-squares`
4×	`associate-/l*`
2×	`associate-l/` `associate-r/` `p16-flip--`
1×	`sub-neg` `associate-/l/`

Calls

4 calls:

Slowest

36.0ms	(-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
28.0ms	(/.p16 (-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (.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 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
5.0ms	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))
5.0ms	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.0ms	(/.p16 (-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (.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 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.0ms	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.0ms	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))

simplify4.3s

Calls

17 calls:

Slowest

1.2s	(-.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)))))))
851.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
760.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
713.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
629.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize122.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.5b	(/.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.3b	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.3b	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

2×	`p16-flip--` `associate-/l*`
1×	`sub-neg` `associate-r/` `-commutative` `associate-/l/`

Calls

4 calls:

Slowest

38.0ms	(/.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
6.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
3.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
3.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(/.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

simplify5.0s

Calls

11 calls:

Slowest

1.1s	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
956.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
919.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
747.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
651.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune457.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize163.0ms

Local error

Found 4 expressions with local error:

0.7b	(-.p16 (.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)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.5b	(/.p16 (-.p16 (.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)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.4b	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))
0.3b	(/.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-l/` `p16-flip--` `-commutative` `associate-/l*` `associate-/l/`
1×	`sub-neg` `associate-*r/`

Calls

4 calls:

Slowest

42.0ms	(/.p16 (-.p16 (.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)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
12.0ms	(/.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1))))
11.0ms	(-.p16 (.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)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1)))))
10.0ms	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(-.p16 (.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)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.0ms	(/.p16 (-.p16 (.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)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.0ms	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))
0.0ms	(/.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1))))

simplify150.0ms

Calls

10 calls:

Slowest

107.0ms	(-.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 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1))))))
7.0ms	(sqrt.p16 (+.p16 x (real->posit16 1)))
7.0ms	(*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 x)))
6.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
6.0ms	(sqrt.p16 (+.p16 x (real->posit16 1)))

prune494.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.6b

regimes349.0ms

Accuracy

-∞% (-62.8b remaining)

Error of 1.2b against oracle of 64.0b and baseline of 64.0b

bsearch3.0ms

end0.0ms

sample4.3s

Algorithm

halfpoints

Results