Details

Time bar (total: 24.8s)

sample256.0ms

Algorithm
halfpoints

simplify2.2s

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

prune55.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize281.0ms

Local error

Found 4 expressions with local error:

0.2b
(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
0.2b
(/.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))))
0.4b
(+.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))))

rewrite364.0ms

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:
63.0ms
(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
117.0ms
(/.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))))
16.0ms
(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
150.0ms
(/.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))))

simplify4.1s

Counts
410 → 410
Iterations
IterNodes
done5001
34067
2517
1116
055

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize390.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.p16 (/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (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)) beta alpha) (real->posit16 1.0) (real->posit16 1.0))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
7.0b
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (real->posit16 1.0) (real->posit16 1.0))
9.4b
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha)

rewrite55.0ms

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:
41.0ms
(/.p16 (/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (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))))
11.0ms
(/.p16 (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (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)) beta alpha) (real->posit16 1.0) (real->posit16 1.0))
0.0ms
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha)

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)) beta alpha) (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)) beta alpha) (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)) beta alpha) (real->posit16 1.0) (real->posit16 1.0))
0.0ms
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha)

simplify1.1s

Counts
94 → 94
Iterations
IterNodes
done5035
31302
2271
174
039

prune989.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize409.0ms

Local error

Found 4 expressions with local error:

0.3b
(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.7b
(/.p16 (+.p16 beta (+.p16 alpha (*.p16 (real->posit16 2) (real->posit16 1)))) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (real->posit16 1.0) (real->posit16 1.0))))
7.0b
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (real->posit16 1.0) (real->posit16 1.0))
9.4b
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
18×*p16-lft-identity-expand p16-times-frac *p16-rgt-identity-expand p16-*-un-lft-identity
6×associate-/r* /p16-rgt-identity-expand associate-/l*
2×+p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand associate-/r/ +p16-rgt-identity-expand associate-/l/
Counts
4 → 50
Calls
4 calls:
16.0ms
(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
11.0ms
(/.p16 (+.p16 beta (+.p16 alpha (*.p16 (real->posit16 2) (real->posit16 1)))) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (real->posit16 1.0) (real->posit16 1.0))))
0.0ms
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (real->posit16 1.0) (real->posit16 1.0))
0.0ms
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha)

series0.0ms

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

simplify1.8s

Counts
54 → 54
Iterations
IterNodes
done5005
42112
3470
2165
154
034

prune844.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize464.0ms

Local error

Found 4 expressions with local error:

0.3b
(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.7b
(*.p16 (/.p16 (real->posit16 1.0) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (real->posit16 1.0) (real->posit16 1.0)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 1) (real->posit16 2))))
7.0b
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (real->posit16 1.0) (real->posit16 1.0))
9.4b
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
18×*p16-lft-identity-expand p16-times-frac *p16-rgt-identity-expand p16-*-un-lft-identity
13×associate-*l*
6×/p16-rgt-identity-expand
3×associate-/r* associate-*r* associate-/l*
2×+p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand associate-/r/ +p16-rgt-identity-expand
1×distribute-rgt-in distribute-lft-in associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 54
Calls
4 calls:
15.0ms
(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
7.0ms
(*.p16 (/.p16 (real->posit16 1.0) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (real->posit16 1.0) (real->posit16 1.0)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 1) (real->posit16 2))))
0.0ms
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (real->posit16 1.0) (real->posit16 1.0))
0.0ms
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha)

series0.0ms

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

simplify2.0s

Counts
58 → 58
Iterations
IterNodes
done5000
31774
2328
193
037

prune961.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes822.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done24
124
022

end0.0ms

sample5.9s

Algorithm
halfpoints