Details

Time bar (total: 5.9s)

sample94.0ms

Algorithm
halfpoints
Results

simplify58.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
58.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize106.0ms

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)))

rewrite3.0ms

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)))

simplify146.0ms

Counts
2 → 4
Calls
2 calls:
Slowest
76.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
70.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune69.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize193.0ms

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))

rewrite19.0ms

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 (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 (*.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)))
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))

simplify204.0ms

Counts
5 → 13
Calls
5 calls:
Slowest
92.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
83.0ms
(-.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))))
14.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
11.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
2.0ms
(real->posit16 1)

prune467.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize360.0ms

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))

rewrite19.0ms

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
11.0ms
(/.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 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))

simplify1.1s

Counts
11 → 14
Calls
11 calls:
Slowest
260.0ms
(/.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)))))
238.0ms
(/.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)))))
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)))))
61.0ms
(*.p16 (*.p16 (sqrt.p16 x) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))

prune496.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize168.0ms

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))

simplify544.0ms

Counts
3 → 4
Calls
3 calls:
Slowest
210.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))
187.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))
146.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))

prune74.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes118.0ms

Accuracy

-∞% (-63.8b remaining)

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

bsearch3.0ms

end0.0ms

sample1.6s

Algorithm
halfpoints
Results