Details

sample272.0ms

Algorithm

halfpoints

Results

simplify818.0ms

Calls

1 calls:

Slowest

818.0ms

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

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize206.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.3b	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b	(/.p16 (real->posit16 1) (sqrt.p16 x))
0.1b	(sqrt.p16 (+.p16 x (real->posit16 1)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

1×	`sub-neg` `p16-flip--`

Calls

4 calls:

Slowest

3.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
1.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
1.0ms	(/.p16 (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 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms	(sqrt.p16 (+.p16 x (real->posit16 1)))
0.0ms	(/.p16 (real->posit16 1) (sqrt.p16 x))

simplify2.9s

Calls

4 calls:

Slowest

795.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
795.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
698.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
580.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune303.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.9b

localize256.0ms

Local error

Found 4 expressions with local error:

0.7b	(-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.5b	(/.p16 (-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.4b	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))
0.3b	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

55.0ms	(/.p16 (-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
24.0ms	(-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
10.0ms	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))
10.0ms	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

series0.0ms

Calls

4 calls:

Slowest

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

simplify4.9s

Calls

17 calls:

Slowest

1.2s	(-.p16 (.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))) (.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))))
964.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
905.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
877.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
861.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize114.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.5b	(/.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.3b	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.3b	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

45.0ms	(/.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
6.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
3.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
3.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

series0.0ms

Calls

4 calls:

Slowest

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

simplify4.6s

Calls

11 calls:

Slowest

859.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
803.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
776.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
734.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
703.0ms	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune520.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize175.0ms

Local error

Found 4 expressions with local error:

0.7b	(-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (/.p16 (.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.5b	(/.p16 (-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (/.p16 (.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.4b	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))
0.3b	(/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

21.0ms	(/.p16 (-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (/.p16 (.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
12.0ms	(-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (/.p16 (.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1)))))
6.0ms	(/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1))))
5.0ms	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))

series0.0ms

Calls

4 calls:

Slowest

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

simplify166.0ms

Calls

10 calls:

Slowest

116.0ms	(-.p16 (.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))) (.p16 (/.p16 (.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1))))))
8.0ms	(*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
8.0ms	(*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
8.0ms	(*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
7.0ms	(*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune495.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.6b

regimes415.0ms

Accuracy

-∞% (-62.8b remaining)

Error of 1.2b against oracle of 64.0b and baseline of 64.0b

bsearch5.0ms

end0.0ms

sample5.4s

Algorithm

halfpoints

Results