Details

Time bar (total: 6.5s)

sample58.0ms

Algorithm
halfpoints
Results

simplify62.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
62.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize124.0ms

Local error

Found 2 expressions with local error:

0.8b
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
0.0b
(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
3.0ms
(-.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)))

simplify157.0ms

Counts
2 → 4
Calls
2 calls:
Slowest
82.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
74.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune118.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize245.0ms

Local error

Found 4 expressions with local error:

0.4b
(-.p16 (*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
0.3b
(*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b
(/.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)))
0.1b
(*.p16 (sqrt.p16 x) (sqrt.p16 x))

rewrite25.0ms

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)))
7.0ms
(-.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 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1))))
4.0ms
(*.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))

simplify182.0ms

Counts
5 → 13
Calls
5 calls:
Slowest
81.0ms
(-.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))))
70.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
15.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
12.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
2.0ms
(real->posit16 1)

prune541.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize341.0ms

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

rewrite13.0ms

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))))
3.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
2.0ms
(*.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 (+.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))

simplify1.2s

Counts
11 → 14
Calls
11 calls:
Slowest
271.0ms
(/.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)))))
250.0ms
(/.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)))))
227.0ms
(/.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)))))
209.0ms
(/.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)))))
72.0ms
(*.p16 (*.p16 (sqrt.p16 x) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))

prune539.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize238.0ms

Local error

Found 3 expressions with local error:

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

simplify591.0ms

Counts
3 → 4
Calls
3 calls:
Slowest
240.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))
180.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))
170.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))

prune121.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes196.0ms

Accuracy

-∞% (-63.8b remaining)

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

bsearch5.0ms

end0.0ms

sample1.8s

Algorithm
halfpoints
Results