Details

sample274.0ms

Algorithm

halfpoints

Results

simplify89.0ms

Calls

1 calls:

Slowest

89.0ms

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

prune43.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize193.0ms

Local error

Found 2 expressions with local error:

1.4b	(-.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)))

simplify167.0ms

Calls

2 calls:

Slowest

89.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
77.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune237.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.9b

localize281.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.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)))
0.2b	(*.p16 (sqrt.p16 x) (sqrt.p16 x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

23.0ms	(/.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)))
12.0ms	(-.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 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1))))
4.0ms	(*.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))

simplify606.0ms

Calls

14 calls:

Slowest

125.0ms	(-.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))))
99.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
96.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
89.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
86.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize74.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.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)))
0.2b	(*.p16 (sqrt.p16 x) (sqrt.p16 x))
0.2b	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

20.0ms	(/.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)))
14.0ms	(-.p16 (+.p16 x (real->posit16 1)) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
6.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
5.0ms	(*.p16 (sqrt.p16 x) (sqrt.p16 x))

series1.0ms

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))

simplify157.0ms

Calls

6 calls:

Slowest

146.0ms	(-.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)

prune950.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

localize186.0ms

Local error

Found 4 expressions with local error:

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

1×	`+-commutative` `sub-neg` `p16-flip--` `*-commutative` `sqrt-sqrd.p16`

Calls

4 calls:

Slowest

14.0ms	(/.p16 (+.p16 (real->posit16 1) (-.p16 x (*.p16 (sqrt.p16 x) (sqrt.p16 x)))) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))
6.0ms	(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
5.0ms	(-.p16 x (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
4.0ms	(*.p16 (sqrt.p16 x) (sqrt.p16 x))

series0.0ms

Calls

4 calls:

Slowest

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

simplify9.0ms

Calls

4 calls:

Slowest

2.0ms	(real->posit16 1)
2.0ms	(real->posit16 1)
2.0ms	(real->posit16 1)
2.0ms	(real->posit16 1)

prune691.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes378.0ms

Accuracy

-∞% (-63.6b remaining)

Error of 0.4b against oracle of 64.0b and baseline of 64.0b

bsearch2.0ms

end0.0ms

sample5.0s

Algorithm

halfpoints

Results