Details

Time bar (total: 5.8s)

sample58.0ms

Algorithm
halfpoints
Results

simplify67.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
67.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize75.0ms

Local error

Found 2 expressions with local error:

0.9b
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
0.1b
(sqrt.p16 (+.p16 x (real->posit16 1)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg p16-flip--
Counts
2 → 2
Calls
2 calls:
Slowest
2.0ms
(-.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)))

simplify189.0ms

Counts
2 → 4
Calls
2 calls:
Slowest
98.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
90.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune65.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize164.0ms

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))
0.2b
(/.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)))

rewrite33.0ms

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
16.0ms
(-.p16 (*.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (*.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)))
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 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1))))
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 x) (sqrt.p16 x))

simplify199.0ms

Counts
5 → 13
Calls
5 calls:
Slowest
100.0ms
(-.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))))
66.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
16.0ms
(+.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)

prune422.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize148.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip--
1×+-commutative sub-neg associate--l+ *-commutative sqrt-sqrd.p16 associate-/l/
Counts
4 → 7
Calls
4 calls:
Slowest
17.0ms
(/.p16 (-.p16 (+.p16 x (real->posit16 1)) (*.p16 (sqrt.p16 x) (sqrt.p16 x))) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))
8.0ms
(-.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 x))
2.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(-.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 (-.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 x))

simplify123.0ms

Counts
5 → 11
Calls
5 calls:
Slowest
114.0ms
(-.p16 (*.p16 (+.p16 x (real->posit16 1)) (+.p16 x (real->posit16 1))) (*.p16 (*.p16 (sqrt.p16 x) (sqrt.p16 x)) (*.p16 (sqrt.p16 x) (sqrt.p16 x))))
2.0ms
(real->posit16 1)
2.0ms
(real->posit16 1)
2.0ms
(real->posit16 1)
2.0ms
(real->posit16 1)

prune525.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize185.0ms

Local error

Found 4 expressions with local error:

0.5b
(-.p16 (+.p16 x (real->posit16 1)) x)
0.2b
(/.p16 (-.p16 (+.p16 x (real->posit16 1)) x) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))
0.1b
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
0.1b
(sqrt.p16 (+.p16 x (real->posit16 1)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip--
1×+-commutative sub-neg associate--l+ associate-/l/
Counts
4 → 5
Calls
4 calls:
Slowest
22.0ms
(-.p16 (+.p16 x (real->posit16 1)) x)
21.0ms
(/.p16 (-.p16 (+.p16 x (real->posit16 1)) x) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))
5.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (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 x (real->posit16 1)) x)
0.0ms
(/.p16 (-.p16 (+.p16 x (real->posit16 1)) x) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))
0.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))

simplify1.1s

Counts
1 → 9
Calls
1 calls:
Slowest
1.1s
(-.p16 (*.p16 (+.p16 x (real->posit16 1)) (+.p16 x (real->posit16 1))) (*.p16 x x))

prune230.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes89.0ms

Accuracy

-∞% (-63.7b remaining)

Error of 0.3b against oracle of 64.0b and baseline of 64.0b

bsearch2.0ms

end0.0ms

sample2.0s

Algorithm
halfpoints
Results