Details

sample167.0ms

Algorithm

halfpoints

Results

simplify63.0ms

Calls

1 calls:

Slowest

63.0ms

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

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.6b

localize590.0ms

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)))

simplify155.0ms

Calls

2 calls:

Slowest

90.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
65.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune195.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.9b

localize305.0ms

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)))
0.4b	(*.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 x) (sqrt.p16 x))

rewrite12.0ms

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

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

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))

simplify144.0ms

Calls

5 calls:

Slowest

72.0ms	(-.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))))
55.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
7.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
7.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
1.0ms	(real->posit16 1)

prune617.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize413.0ms

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))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

13.0ms	(-.p16 (+.p16 x (real->posit16 1)) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
12.0ms	(/.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 (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 x) (sqrt.p16 x))
0.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

simplify84.0ms

Calls

5 calls:

Slowest

78.0ms	(-.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)

prune577.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize358.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

10.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
5.0ms	(/.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)))
3.0ms	(+.p16 x (-.p16 (real->posit16 1) (*.p16 (sqrt.p16 x) (sqrt.p16 x))))
2.0ms	(*.p16 (sqrt.p16 x) (sqrt.p16 x))

series0.0ms

Calls

4 calls:

Slowest

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 x (-.p16 (real->posit16 1) (*.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	(neg.p16 (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
1.0ms	(*.p16 (sqrt.p16 x) (sqrt.p16 x))

prune422.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes240.0ms

Accuracy

-∞% (-63.3b remaining)

Error of 0.7b against oracle of 64.0b and baseline of 64.0b

bsearch2.0ms

end0.0ms

sample4.7s

Algorithm

halfpoints

Results