Details

Time bar (total: 8.1s)

sample113.0ms

Algorithm
halfpoints
Results

simplify96.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
96.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize156.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg p16-flip--
Counts
2 → 2
Calls
2 calls:
Slowest
4.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))

series0.0ms

Counts
2 → 2
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)))

simplify203.0ms

Counts
2 → 4
Calls
2 calls:
Slowest
105.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
98.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune138.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize310.0ms

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))))
0.2b
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
0.1b
(/.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)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip-- *-commutative sqrt-sqrd.p16 difference-of-squares
1×sub-neg associate-/l* associate-/l/
Counts
4 → 9
Calls
4 calls:
Slowest
10.0ms
(/.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)))
6.0ms
(-.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 x) (sqrt.p16 x))
4.0ms
(*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1))))

series0.0ms

Counts
4 → 4
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))

simplify258.0ms

Counts
5 → 13
Calls
5 calls:
Slowest
137.0ms
(-.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))))
82.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
28.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
8.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
1.0ms
(real->posit16 1)

prune549.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize536.0ms

Local error

Found 4 expressions with local error:

0.4b
(/.p16 (*.p16 (+.p16 (real->posit16 0.0) (real->posit16 1)) (+.p16 (+.p16 x x) (real->posit16 1))) (*.p16 (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)) (+.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))))
0.2b
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
0.1b
(sqrt.p16 (+.p16 x (real->posit16 1)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
2×*-commutative sqrt-sqrd.p16
1×associate-/r* p16-times-frac associate-/l*
Counts
4 → 7
Calls
4 calls:
Slowest
8.0ms
(/.p16 (*.p16 (+.p16 (real->posit16 0.0) (real->posit16 1)) (+.p16 (+.p16 x x) (real->posit16 1))) (*.p16 (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)) (+.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))))
3.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))

series0.0ms

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

simplify1.4s

Counts
9 → 11
Calls
9 calls:
Slowest
321.0ms
(/.p16 (*.p16 (+.p16 (real->posit16 0.0) (real->posit16 1)) (+.p16 (+.p16 x x) (real->posit16 1))) (*.p16 (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)) (+.p16 (*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))))
319.0ms
(/.p16 (*.p16 (+.p16 (real->posit16 0.0) (real->posit16 1)) (+.p16 (+.p16 x x) (real->posit16 1))) (*.p16 (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)) (+.p16 (*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))))
303.0ms
(/.p16 (*.p16 (+.p16 (real->posit16 0.0) (real->posit16 1)) (+.p16 (+.p16 x x) (real->posit16 1))) (*.p16 (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)) (+.p16 (*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))))
290.0ms
(/.p16 (*.p16 (+.p16 (real->posit16 0.0) (real->posit16 1)) (+.p16 (+.p16 x x) (real->posit16 1))) (*.p16 (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)) (+.p16 (*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))))
55.0ms
(/.p16 (+.p16 (real->posit16 0.0) (real->posit16 1)) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))

prune597.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize236.0ms

Local error

Found 3 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative
Counts
3 → 1
Calls
3 calls:
Slowest
5.0ms
(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
4.0ms
(/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.0ms
(sqrt.p16 (+.p16 (real->posit16 1) x))

series0.0ms

Counts
3 → 3
Calls
3 calls:
Slowest
0.0ms
(/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.0ms
(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.0ms
(sqrt.p16 (+.p16 (real->posit16 1) x))

simplify772.0ms

Counts
3 → 4
Calls
3 calls:
Slowest
257.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))
257.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))
257.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))

prune109.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes192.0ms

Accuracy

-∞% (-63.8b remaining)

Error of 0.2b against oracle of 64.0b and baseline of 64.0b

bsearch5.0ms

end0.0ms

sample2.4s

Algorithm
halfpoints
Results