Details

Time bar (total: 6.3s)

sample80.0ms

Algorithm
halfpoints
Results

simplify76.0ms

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize103.0ms

Local error

Found 2 expressions with local error:

0.8b
(-.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)))

simplify166.0ms

Counts
2 → 4
Calls
2 calls:
Slowest
92.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
74.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

prune122.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize243.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
2×*-commutative sqrt-sqrd.p16
1×+-commutative sub-neg p16-flip-- difference-of-squares
Counts
4 → 8
Calls
4 calls:
Slowest
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)))
5.0ms
(+.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 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 (+.p16 x (real->posit16 1))))
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 x))
0.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))

simplify121.0ms

Counts
3 → 12
Calls
3 calls:
Slowest
104.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
14.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
2.0ms
(real->posit16 1)

prune412.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize207.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

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
20.0ms
(/.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)))
13.0ms
(-.p16 (+.p16 x (real->posit16 1)) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
6.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
4.0ms
(*.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 (-.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))
0.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

simplify124.0ms

Counts
5 → 11
Calls
5 calls:
Slowest
118.0ms
(-.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))))
1.0ms
(real->posit16 1)
1.0ms
(real->posit16 1)
1.0ms
(real->posit16 1)
1.0ms
(real->posit16 1)

prune337.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

localize231.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip--
1×+-commutative sub-neg associate--l+ associate-/l/
Counts
4 → 5
Calls
4 calls:
Slowest
20.0ms
(/.p16 (-.p16 (+.p16 x (real->posit16 1)) x) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))
11.0ms
(-.p16 (+.p16 x (real->posit16 1)) 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
(sqrt.p16 (+.p16 x (real->posit16 1)))
0.0ms
(+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))
0.0ms
(/.p16 (-.p16 (+.p16 x (real->posit16 1)) x) (+.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x)))

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))

prune240.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes132.0ms

Accuracy

-∞% (-63.7b remaining)

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

bsearch5.0ms

end0.0ms

sample2.5s

Algorithm
halfpoints
Results