Details

Time bar (total: 9.4s)

sample123.0ms

Algorithm
halfpoints
Results

simplify276.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
275.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize201.0ms

Local error

Found 4 expressions with local error:

0.7b
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
0.3b
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.2b
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.1b
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
2×sub-neg p16-flip--
1×+-commutative associate-+l+ associate-/r/ associate-+l-
Counts
4 → 6
Calls
4 calls:
Slowest
15.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
3.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
2.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
2.0ms
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
0.0ms
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))

simplify978.0ms

Counts
7 → 10
Calls
7 calls:
Slowest
316.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
220.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
212.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
202.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
15.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))

prune263.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize181.0ms

Local error

Found 4 expressions with local error:

0.8b
(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (+.p16 (neg.p16 (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))))
0.4b
(+.p16 (neg.p16 (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
0.2b
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.1b
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
2×+-commutative
1×associate-+r+ p16-flip-- associate-/r/
Counts
4 → 4
Calls
4 calls:
Slowest
6.0ms
(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (+.p16 (neg.p16 (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))))
4.0ms
(+.p16 (neg.p16 (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
4.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
3.0ms
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (+.p16 (neg.p16 (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))))
0.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.0ms
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.0ms
(+.p16 (neg.p16 (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))

simplify57.0ms

Counts
6 → 8
Calls
6 calls:
Slowest
24.0ms
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
12.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
6.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
6.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
6.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))

prune274.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.8b

localize301.0ms

Local error

Found 4 expressions with local error:

0.7b
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (+.p16 x (real->posit16 1))))
0.7b
(*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (+.p16 x (real->posit16 1)))
0.3b
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.2b
(/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
3×p16-flip--
2×distribute-rgt-in associate-+r+ sub-neg distribute-lft-in associate-/r/
1×+-commutative associate-+l+ associate-/r* associate-*l* associate-*l/ *-commutative associate-+l- difference-of-squares
Counts
4 → 14
Calls
4 calls:
Slowest
23.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (+.p16 x (real->posit16 1))))
13.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
6.0ms
(*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (+.p16 x (real->posit16 1)))
3.0ms
(/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (+.p16 x (real->posit16 1))))
0.0ms
(*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (+.p16 x (real->posit16 1)))
0.0ms
(/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1))))
0.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))

simplify1.5s

Counts
14 → 18
Calls
14 calls:
Slowest
424.0ms
(/.p16 (real->posit16 1) (-.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 (*.p16 (real->posit16 1) (real->posit16 1)) (*.p16 (real->posit16 1) (real->posit16 1)))))
269.0ms
(*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (real->posit16 1))
264.0ms
(*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))))
246.0ms
(*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (real->posit16 1))
202.0ms
(*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))))

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize432.0ms

Local error

Found 4 expressions with local error:

0.7b
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (*.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))))
0.6b
(/.p16 (*.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1))))
0.3b
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.2b
(-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
3×sub-neg p16-flip-- difference-of-squares
1×+-commutative associate-+l+ associate-/r* p16-times-frac associate-/r/ associate-+l- associate-/l*
Counts
4 → 12
Calls
4 calls:
Slowest
26.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (*.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))))
7.0ms
(/.p16 (*.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1))))
6.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
5.0ms
(-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (*.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))))
0.0ms
(/.p16 (*.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1))))
0.0ms
(-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))
0.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))

simplify176.0ms

Counts
13 → 16
Calls
13 calls:
Slowest
28.0ms
(/.p16 (+.p16 x (real->posit16 1)) (-.p16 x (real->posit16 1)))
20.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
17.0ms
(*.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
15.0ms
(*.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
15.0ms
(*.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))

prune675.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.6b

regimes165.0ms

Accuracy

-∞% (-63.0b remaining)

Error of 1.0b against oracle of 64.0b and baseline of 64.0b

bsearch11.0ms

end0.0ms

sample2.6s

Algorithm
halfpoints
Results