Details

Time bar (total: 7.6s)

sample87.0ms

Algorithm
halfpoints
Results

simplify83.0ms

Calls
1 calls:
Slowest
83.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize161.0ms

Local error

Found 2 expressions with local error:

0.7b
(-.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--
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

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)))

simplify190.0ms

Calls
2 calls:
Slowest
98.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
92.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune134.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize173.0ms

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 (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)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip-- *-commutative sqrt-sqrd.p16 difference-of-squares
1×sub-neg associate-/l* associate-/l/
Calls
4 calls:
Slowest
13.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
9.0ms
(/.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)))
3.0ms
(*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1))))

series0.0ms

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))

simplify265.0ms

Calls
5 calls:
Slowest
144.0ms
(-.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))))
92.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
13.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
13.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
2.0ms
(real->posit16 1)

prune555.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize293.0ms

Local error

Found 4 expressions with local error:

0.3b
(/.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))))
0.2b
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
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))))

rewrite26.0ms

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*
Calls
4 calls:
Slowest
9.0ms
(/.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)))))
8.0ms
(*.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))))
5.0ms
(*.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

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))

simplify1.3s

Calls
11 calls:
Slowest
329.0ms
(/.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)))))
293.0ms
(/.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)))))
268.0ms
(/.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)))))
236.0ms
(/.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)))))
59.0ms
(*.p16 (*.p16 (sqrt.p16 x) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))

prune708.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize209.0ms

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative
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

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

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))
156.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))
147.0ms
(*.p16 (/.p16 (real->posit16 1) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (real->posit16 1.0))

prune140.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes194.0ms

Accuracy

-∞% (-63.8b remaining)

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

bsearch5.0ms

end0.0ms

sample2.5s

Algorithm
halfpoints
Results