Details

Time bar (total: 12.9s)

sample140.0ms

Algorithm
halfpoints
Results

simplify53.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
53.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize246.0ms

Local error

Found 2 expressions with local error:

1.3b
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
0.1b
(sqrt.p16 (+.p16 x (real->posit16 1)))

rewrite4.0ms

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)))

simplify178.0ms

Counts
2 → 4
Calls
2 calls:
Slowest
89.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
88.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune208.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.9b

localize394.0ms

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 (sqrt.p16 x) (sqrt.p16 x))
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)))

rewrite13.0ms

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
5.0ms
(/.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)))
3.0ms
(-.p16 (*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
2.0ms
(*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))

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))

simplify151.0ms

Counts
5 → 13
Calls
5 calls:
Slowest
78.0ms
(-.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))))
56.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
8.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
7.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
1.0ms
(real->posit16 1)

prune619.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize799.0ms

Local error

Found 4 expressions with local error:

0.8b
(/.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))))
0.3b
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
0.3b
(*.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))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
3×*-commutative
2×sqrt-sqrd.p16
1×distribute-rgt-in associate-/r* distribute-lft-in p16-times-frac associate-/l*
Counts
4 → 10
Calls
4 calls:
Slowest
4.0ms
(/.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 (+.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))))
2.0ms
(*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))

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

simplify842.0ms

Counts
11 → 14
Calls
11 calls:
Slowest
205.0ms
(/.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)))))
204.0ms
(/.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)))))
157.0ms
(/.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)))))
154.0ms
(/.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)))))
41.0ms
(*.p16 (*.p16 (sqrt.p16 x) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize371.0ms

Local error

Found 3 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative
Counts
3 → 1
Calls
3 calls:
Slowest
2.0ms
(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
2.0ms
(/.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))

simplify506.0ms

Counts
3 → 4
Calls
3 calls:
Slowest
222.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))
164.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))
120.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))

prune175.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes486.0ms

Accuracy

-∞% (-63.6b remaining)

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

bsearch5.0ms

end0.0ms

sample6.3s

Algorithm
halfpoints
Results