Details

sample155.0ms

Algorithm

halfpoints

Results

simplify62.0ms

Calls

1 calls:

Slowest

62.0ms

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

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize129.0ms

Local error

Found 2 expressions with local error:

1.3b	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
0.1b	(sqrt.p16 (+.p16 x (real->posit16 1)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

1×	`sub-neg` `p16-flip--`

Calls

2 calls:

Slowest

2.0ms	(-.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)))

simplify152.0ms

Calls

2 calls:

Slowest

89.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
63.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune153.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize175.0ms

Local error

Found 4 expressions with local error:

0.5b	(-.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 (-.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)))
0.3b	(*.p16 (sqrt.p16 x) (sqrt.p16 x))

rewrite23.0ms

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

9.0ms	(/.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)))
6.0ms	(-.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))

simplify259.0ms

Calls

5 calls:

Slowest

131.0ms	(-.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))))
97.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
14.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
13.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
2.0ms	(real->posit16 1)

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize102.0ms

Local error

Found 4 expressions with local error:

0.5b	(-.p16 (+.p16 x (real->posit16 1)) (*.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)))
0.3b	(*.p16 (sqrt.p16 x) (sqrt.p16 x))
0.2b	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

rewrite24.0ms

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

simplify104.0ms

Calls

5 calls:

Slowest

99.0ms	(-.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))))
1.0ms	(real->posit16 1)
1.0ms	(real->posit16 1)
1.0ms	(real->posit16 1)
1.0ms	(real->posit16 1)

prune639.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

localize81.0ms

Local error

Found 4 expressions with local error:

0.5b	(-.p16 (+.p16 x (real->posit16 1)) x)
0.3b	(/.p16 (-.p16 (+.p16 x (real->posit16 1)) 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))
0.1b	(sqrt.p16 (+.p16 x (real->posit16 1)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

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

4 calls:

Slowest

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

simplify639.0ms

Calls

1 calls:

Slowest

638.0ms

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

prune367.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

regimes385.0ms

Accuracy

-∞% (-63.4b remaining)

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

bsearch5.0ms

end0.0ms

sample4.5s

Algorithm

halfpoints

Results