Details

sample243.0ms

Algorithm

halfpoints

Results

simplify77.0ms

Calls

1 calls:

Slowest

77.0ms

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

prune60.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize217.0ms

Local error

Found 2 expressions with local error:

1.7b	(-.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)))

simplify175.0ms

Calls

2 calls:

Slowest

103.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
72.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune204.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.1b

localize253.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.p16 (.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (.p16 (sqrt.p16 x) (sqrt.p16 x)))
0.4b	(*.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 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

11.0ms	(/.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)))
5.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
4.0ms	(*.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 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

simplify241.0ms

Calls

5 calls:

Slowest

116.0ms	(-.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))))
92.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
15.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
14.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
2.0ms	(real->posit16 1)

prune716.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize104.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.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 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
0.3b	(*.p16 (sqrt.p16 x) (sqrt.p16 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

5.0ms	(/.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)))
3.0ms	(-.p16 (+.p16 x (real->posit16 1)) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
3.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
2.0ms	(*.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))

simplify98.0ms

Calls

5 calls:

Slowest

92.0ms	(-.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)

prune724.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.4b

localize126.0ms

Local error

Found 4 expressions with local error:

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

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

simplify7.0ms

Calls

2 calls:

Slowest

4.0ms	(neg.p16 (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
3.0ms	(*.p16 (sqrt.p16 x) (sqrt.p16 x))

prune588.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.4b

regimes442.0ms

Accuracy

-∞% (-63.4b remaining)

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

bsearch4.0ms

end0.0ms

sample6.8s

Algorithm

halfpoints

Results