Details

Time bar (total: 12.4s)

sample71.0ms

Algorithm
halfpoints
Results

simplify758.0ms

Calls
1 calls:
Slowest
758.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize226.0ms

Local error

Found 4 expressions with local error:

0.4b
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.1b
(/.p16 (real->posit16 1) (sqrt.p16 x))
0.1b
(sqrt.p16 (+.p16 x (real->posit16 1)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg p16-flip--
Calls
4 calls:
Slowest
5.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 x))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
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
(/.p16 (real->posit16 1) (sqrt.p16 x))
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))

simplify3.7s

Calls
4 calls:
Slowest
1.1s
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
1.1s
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
832.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
716.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune118.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize108.0ms

Local error

Found 4 expressions with local error:

0.4b
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.3b
(-.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))))))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg associate-*l/ associate-*r/ p16-flip-- *-commutative difference-of-squares
Calls
4 calls:
Slowest
2.0ms
(-.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))))))
2.0ms
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.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 (+.p16 x (real->posit16 1))))

series0.0ms

Calls
4 calls:
Slowest
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)))))
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 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

simplify1.1s

Calls
4 calls:
Slowest
1.0s
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
17.0ms
(*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
16.0ms
(+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
11.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))

prune391.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize87.0ms

Local error

Found 4 expressions with local error:

0.4b
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg p16-flip--
Calls
4 calls:
Slowest
6.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms
(/.p16 (real->posit16 1) (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
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

simplify3.0s

Calls
8 calls:
Slowest
1.1s
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
690.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
641.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
559.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
23.0ms
(+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune111.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg associate-*l/ p16-flip-- associate-/l* associate-/l/
Calls
4 calls:
Slowest
3.0ms
(-.p16 (*.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)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1)))))
2.0ms
(/.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (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 (+.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 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.0ms
(/.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (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))))

simplify40.0ms

Calls
6 calls:
Slowest
13.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
6.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))
6.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))
6.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))
5.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))

prune331.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.3b

regimes154.0ms

Accuracy

-∞% (-63.5b remaining)

Error of 0.5b against oracle of 64.0b and baseline of 64.0b

bsearch3.0ms

end0.0ms

sample2.0s

Algorithm
halfpoints
Results