Details

Time bar (total: 1.1m)

sample93.0ms

Algorithm
halfpoints
Results

simplify18.2s

Counts
1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize125.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg p16-flip--
Counts
4 → 2
Calls
4 calls:
Slowest
3.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 x))
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 x))
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))

simplify16.1s

Counts
6 → 6

prune85.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize194.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip-- difference-of-squares
1×sub-neg associate-*l/ associate-*r/ *-commutative associate-/l* associate-/l/
Counts
4 → 8
Calls
4 calls:
Slowest
7.0ms
(/.p16 (-.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
3.0ms
(-.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
2.0ms
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
1.0ms
(/.p16 (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 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.0ms
(/.p16 (-.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.0ms
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

simplify1.7s

Counts
12 → 12

prune247.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize180.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip--
1×sub-neg associate-*r/ associate-/l* associate-/l/
Counts
4 → 4
Calls
4 calls:
Slowest
8.0ms
(/.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
3.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

series6.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
6.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.0ms
(/.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

simplify13.3s

Counts
8 → 8

prune154.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize156.0ms

Local error

Found 4 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg p16-flip--
Counts
4 → 2
Calls
4 calls:
Slowest
3.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

simplify12.7s

Counts
6 → 6

prune70.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.3b

regimes88.0ms

Accuracy

0% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 0.6b

bsearch5.0ms

end0.0ms

sample1.5s

Algorithm
halfpoints
Results