Details

Time bar (total: 17.0s)

sample123.0ms

Algorithm
halfpoints
Results

simplify1.1s

Counts
1 → 1
Calls
1 calls:
Slowest
1.1s
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize222.0ms

Local error

Found 4 expressions with local error:

0.5b
(-.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 x))
0.1b
(sqrt.p16 (+.p16 x (real->posit16 1)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg p16-flip--
Counts
4 → 2
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 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

Counts
4 → 4
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))

simplify4.5s

Counts
4 → 6
Calls
4 calls:
Slowest
1.5s
(-.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)))))
1.0s
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
811.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune176.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize247.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip-- difference-of-squares
1×sub-neg associate-*l/ associate-*r/ *-commutative associate-/l* associate-/l/
Counts
4 → 8
Calls
4 calls:
Slowest
14.0ms
(/.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))))))
3.0ms
(-.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))))

series0.0ms

Counts
4 → 4
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 (+.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))))

simplify2.2s

Counts
6 → 12
Calls
6 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)))))))
1.0s
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
16.0ms
(*.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)))

prune472.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize313.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip--
1×sub-neg associate-*r/ associate-/l* associate-/l/
Counts
4 → 4
Calls
4 calls:
Slowest
16.0ms
(/.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)))))
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

Counts
4 → 4
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))))

simplify4.7s

Counts
10 → 8
Calls
10 calls:
Slowest
1.1s
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
1.0s
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
953.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
935.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
646.0ms
(*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (-.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)))))))

prune197.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize384.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip-- associate-/l/
1×sub-neg associate-*l/ associate-/l*
Counts
4 → 5
Calls
4 calls:
Slowest
16.0ms
(/.p16 (-.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))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
8.0ms
(-.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)))))
4.0ms
(/.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 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

series0.0ms

Counts
4 → 4
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 (/.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))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (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))))

simplify191.0ms

Counts
7 → 9
Calls
7 calls:
Slowest
149.0ms
(-.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 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1))))))
6.0ms
(/.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)))
5.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))

prune286.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

regimes159.0ms

Accuracy

-∞% (-63.4b remaining)

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

bsearch2.0ms

end0.0ms

sample1.7s

Algorithm
halfpoints
Results