Details

sample269.0ms

Algorithm

halfpoints

Results

simplify118.0ms

Calls

1 calls:

Slowest

118.0ms

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

prune67.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize250.0ms

Local error

Found 2 expressions with local error:

1.5b	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
0.1b	(sqrt.p16 (+.p16 x (real->posit16 1)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

1×	`sub-neg` `p16-flip--`

Calls

2 calls:

Slowest

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

series0.0ms

Calls

2 calls:

Slowest

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

simplify203.0ms

Calls

2 calls:

Slowest

105.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
98.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune253.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.0b

localize240.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

2×	`p16-flip--` `*-commutative` `sqrt-sqrd.p16` `difference-of-squares`
1×	`sub-neg` `associate-/l*` `associate-/l/`

Calls

4 calls:

Slowest

8.0ms	(/.p16 (-.p16 (.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (.p16 (sqrt.p16 x) (sqrt.p16 x))) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))
5.0ms	(-.p16 (.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (.p16 (sqrt.p16 x) (sqrt.p16 x)))
4.0ms	(*.p16 (sqrt.p16 x) (sqrt.p16 x))
3.0ms	(*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1))))

series0.0ms

Calls

4 calls:

Slowest

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

simplify225.0ms

Calls

5 calls:

Slowest

123.0ms	(-.p16 (.p16 (.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1))))) (.p16 (.p16 (sqrt.p16 x) (sqrt.p16 x)) (.p16 (sqrt.p16 x) (sqrt.p16 x))))
76.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
14.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
8.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
2.0ms	(real->posit16 1)

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize111.0ms

Local error

Found 4 expressions with local error:

0.7b	(-.p16 (+.p16 x (real->posit16 1)) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
0.3b	(*.p16 (sqrt.p16 x) (sqrt.p16 x))
0.3b	(/.p16 (-.p16 (+.p16 x (real->posit16 1)) (*.p16 (sqrt.p16 x) (sqrt.p16 x))) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))
0.2b	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

2×	`p16-flip--`
1×	`+-commutative` `sub-neg` `associate--l+` `*-commutative` `sqrt-sqrd.p16` `associate-/l/`

Calls

4 calls:

Slowest

9.0ms	(/.p16 (-.p16 (+.p16 x (real->posit16 1)) (*.p16 (sqrt.p16 x) (sqrt.p16 x))) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))
7.0ms	(-.p16 (+.p16 x (real->posit16 1)) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
5.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
4.0ms	(*.p16 (sqrt.p16 x) (sqrt.p16 x))

series0.0ms

Calls

4 calls:

Slowest

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

simplify145.0ms

Calls

5 calls:

Slowest

137.0ms	(-.p16 (.p16 (+.p16 x (real->posit16 1)) (+.p16 x (real->posit16 1))) (.p16 (.p16 (sqrt.p16 x) (sqrt.p16 x)) (.p16 (sqrt.p16 x) (sqrt.p16 x))))
2.0ms	(real->posit16 1)
2.0ms	(real->posit16 1)
2.0ms	(real->posit16 1)
2.0ms	(real->posit16 1)

prune847.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize122.0ms

Local error

Found 4 expressions with local error:

0.4b	(+.p16 x (-.p16 (real->posit16 1) (*.p16 (sqrt.p16 x) (sqrt.p16 x))))
0.3b	(*.p16 (sqrt.p16 x) (sqrt.p16 x))
0.3b	(/.p16 (+.p16 x (-.p16 (real->posit16 1) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))
0.2b	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

2×	`+-commutative`
1×	`associate-+r+` `associate-+r-` `sub-neg` `*-commutative` `sqrt-sqrd.p16`

Calls

4 calls:

Slowest

4.0ms	(/.p16 (+.p16 x (-.p16 (real->posit16 1) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))
2.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
2.0ms	(*.p16 (sqrt.p16 x) (sqrt.p16 x))
2.0ms	(+.p16 x (-.p16 (real->posit16 1) (*.p16 (sqrt.p16 x) (sqrt.p16 x))))

series0.0ms

Calls

4 calls:

Slowest

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

simplify4.0ms

Calls

2 calls:

Slowest

2.0ms	(*.p16 (sqrt.p16 x) (sqrt.p16 x))
2.0ms	(neg.p16 (*.p16 (sqrt.p16 x) (sqrt.p16 x)))

prune640.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes470.0ms

Accuracy

-∞% (-63.4b remaining)

Error of 0.6b against oracle of 64.0b and baseline of 64.0b

bsearch11.0ms

end0.0ms

sample5.3s

Algorithm

halfpoints

Results