Details

Time bar (total: 32.7s)

sample939.0ms

Algorithm
halfpoints
Results

simplify761.0ms

Counts
1 → 1

prune107.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize429.0ms

Local error

Found 4 expressions with local error:

1.0b
(/.p16 (*.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (*.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i))))
0.2b
(+.p16 (/.p16 (*.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (*.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))) (real->posit16 1.0))
0.2b
(*.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))
0.2b
(+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
2×+-commutative
1×distribute-rgt-in associate-+l+ associate-/r* distribute-lft-in p16-times-frac associate-*l/ p16-flip-- *-commutative associate-/l* associate-/l/
Counts
4 → 10
Calls
4 calls:
Slowest
23.0ms
(*.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))
15.0ms
(+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i))
6.0ms
(/.p16 (*.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (*.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i))))
6.0ms
(+.p16 (/.p16 (*.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (*.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))) (real->posit16 1.0))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(/.p16 (*.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (*.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i))))
0.0ms
(+.p16 (/.p16 (*.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (*.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))) (real->posit16 1.0))
0.0ms
(*.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))
0.0ms
(+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i))

simplify520.0ms

Counts
14 → 14

prune510.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize349.0ms

Local error

Found 4 expressions with local error:

0.6b
(/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))
0.5b
(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
0.2b
(+.p16 (*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))) (real->posit16 1.0))
0.2b
(*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative associate-*l/ associate-*r/ p16-flip-- *-commutative associate-/l/
Counts
4 → 5
Calls
4 calls:
Slowest
20.0ms
(/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))
13.0ms
(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
8.0ms
(*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i))))
7.0ms
(+.p16 (*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))) (real->posit16 1.0))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))
0.0ms
(+.p16 (*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))) (real->posit16 1.0))
0.0ms
(*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i))))
0.0ms
(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

simplify7.4s

Counts
9 → 9

prune455.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.4b

localize276.0ms

Local error

Found 4 expressions with local error:

0.5b
(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
0.4b
(/.p16 (*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))
0.3b
(*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (+.p16 beta alpha))
0.2b
(+.p16 (/.p16 (*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i))) (real->posit16 1.0))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
2×associate-*l/ associate-/l/
1×distribute-rgt-in +-commutative distribute-lft-in p16-flip-- *-commutative associate-/l*
Counts
4 → 8
Calls
4 calls:
Slowest
69.0ms
(+.p16 (/.p16 (*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i))) (real->posit16 1.0))
23.0ms
(/.p16 (*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))
7.0ms
(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
6.0ms
(*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (+.p16 beta alpha))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
0.0ms
(/.p16 (*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)))
0.0ms
(+.p16 (/.p16 (*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (+.p16 beta alpha)) (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i))) (real->posit16 1.0))
0.0ms
(*.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (+.p16 beta alpha))

simplify2.0s

Counts
12 → 12

prune699.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.4b

localize363.0ms

Local error

Found 4 expressions with local error:

0.5b
(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
0.5b
(/.p16 (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)) (+.p16 beta alpha))
0.2b
(+.p16 (/.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)) (+.p16 beta alpha))) (real->posit16 1.0))
0.2b
(/.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)) (+.p16 beta alpha)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
2×associate-/l/
1×+-commutative p16-flip-- associate-/r/
Counts
4 → 4
Calls
4 calls:
Slowest
41.0ms
(/.p16 (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)) (+.p16 beta alpha))
26.0ms
(/.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)) (+.p16 beta alpha)))
15.0ms
(+.p16 (/.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)) (+.p16 beta alpha))) (real->posit16 1.0))
13.0ms
(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
0.0ms
(+.p16 (/.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)) (+.p16 beta alpha))) (real->posit16 1.0))
0.0ms
(/.p16 (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)) (+.p16 beta alpha)))
0.0ms
(/.p16 (+.p16 (+.p16 (real->posit16 2.0) (+.p16 beta alpha)) (*.p16 (real->posit16 2) i)) (+.p16 beta alpha))

simplify1.4s

Counts
8 → 8

prune420.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.4b

regimes1.1s

Accuracy

-∞% (-63.4b remaining)

Error of 0.6b against oracle of 64.0b and baseline of 64.0b

bsearch8.0ms

end0.0ms

sample14.7s

Algorithm
halfpoints
Results