Details

Time bar (total: 29.3s)

sample376.0ms

Algorithm
halfpoints

simplify2.4s

Counts
1 → 1
Iterations
IterNodes
done5006
43067
3490
2109
139
018

prune48.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize315.0ms

Local error

Found 4 expressions with local error:

0.2b
(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
0.3b
(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.3b
(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.7b
(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))

rewrite279.0ms

Algorithm
rewrite-expression-head
Rules
468×p16-times-frac
372×*p16-lft-identity-expand p16-*-un-lft-identity
338×*p16-rgt-identity-expand
102×p16-distribute-lft-out distribute-lft-out
80×associate-/l*
51×distribute-rgt-out
18×introduce-quire
17×distribute-lft1-in
14×insert-quire-fdp-add
11×/p16-rgt-identity-expand
10×-p16-rgt-identity-expand
8×insert-quire-add
6×associate-/r* +p16-lft-identity-expand associate-/r/ +p16-rgt-identity-expand
5×associate-+l-
4×associate-+r+
3×associate-+r-
2×+-commutative associate-+l+ associate-/l/
Counts
4 → 406
Calls
4 calls:
61.0ms
(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
97.0ms
(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
8.0ms
(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
96.0ms
(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
0.0ms
(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.0ms
(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.0ms
(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))

simplify4.0s

Counts
410 → 410
Iterations
IterNodes
done5001
34067
2517
1116
055

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize422.0ms

Local error

Found 4 expressions with local error:

0.3b
(/.p16 (/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.7b
(/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
7.8b
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))
10.6b
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
84×p16-times-frac
52×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
16×associate-/l*
9×/p16-rgt-identity-expand
6×associate-/r* associate-/r/
2×+p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand +p16-rgt-identity-expand associate-/l/
Counts
4 → 90
Calls
4 calls:
33.0ms
(/.p16 (/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
12.0ms
(/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.0ms
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))
0.0ms
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(/.p16 (/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.0ms
(/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.0ms
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))
0.0ms
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0))

simplify1.7s

Counts
94 → 94
Iterations
IterNodes
done5008
31800
2317
176
040

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize486.0ms

Local error

Found 4 expressions with local error:

0.3b
(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0)))))
0.6b
(/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))))
7.8b
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))
10.6b
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0))

rewrite498.0ms

Algorithm
rewrite-expression-head
Rules
84×p16-times-frac
52×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
16×associate-/r*
9×/p16-rgt-identity-expand
6×associate-/r/ associate-/l*
2×+p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand +p16-rgt-identity-expand associate-/l/
Counts
4 → 90
Calls
4 calls:
18.0ms
(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0)))))
478.0ms
(/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))))
0.0ms
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))
0.0ms
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0)))))
0.0ms
(/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))))
0.0ms
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))
0.0ms
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0))

simplify3.7s

Counts
94 → 94
Iterations
IterNodes
done5192
83560
71499
6663
5376
4267
3158
280
154
034

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize463.0ms

Local error

Found 4 expressions with local error:

0.3b
(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))) (/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))))
0.7b
(/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
7.8b
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))
10.6b
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
402×p16-times-frac
194×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
46×associate-/r*
18×associate-/r/
17×/p16-rgt-identity-expand
6×associate-/l*
2×+p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand +p16-rgt-identity-expand associate-/l/
Counts
4 → 210
Calls
4 calls:
49.0ms
(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))) (/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))))
22.0ms
(/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.0ms
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))
1.0ms
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))) (/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))))
0.0ms
(/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.0ms
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0)) (real->posit16 1.0) (real->posit16 1.0))
0.0ms
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0))

simplify2.2s

Counts
214 → 214
Iterations
IterNodes
done5007
41623
3469
2226
191
047

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes579.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done24
124
022

end0.0ms

sample6.6s

Algorithm
halfpoints