Details

Time bar (total: 29.6s)

sample235.0ms

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

localize387.0ms

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))))

rewrite261.0ms

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:
39.0ms
(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
122.0ms
(/.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))))
9.0ms
(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
79.0ms
(/.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))))

simplify4.7s

Counts
410 → 410
Iterations
IterNodes
done5001
34067
2517
1116
055

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize469.0ms

Local error

Found 4 expressions with local error:

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

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
429×p16-times-frac
317×*p16-lft-identity-expand p16-*-un-lft-identity
291×*p16-rgt-identity-expand
187×associate-*l*
78×p16-distribute-lft-out distribute-lft-out
39×distribute-rgt-out
22×associate-/l*
13×distribute-lft1-in associate-*r* /p16-rgt-identity-expand
7×+p16-lft-identity-expand associate-/r/ +p16-rgt-identity-expand
6×associate-/r* introduce-quire -p16-rgt-identity-expand
2×distribute-rgt-in associate-+r+ distribute-lft-in associate-/l/
1×+-commutative associate-+l+ associate-+r- insert-quire-add associate-*l/ associate-*r/ *-commutative insert-quire-fdp-add associate-+l-
Counts
4 → 345
Calls
4 calls:
11.0ms
(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
70.0ms
(*.p16 (/.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)))) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha)))
10.0ms
(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
83.0ms
(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))

series1.0ms

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

simplify2.3s

Counts
349 → 349
Iterations
IterNodes
done5068
32119
2509
1136
057

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize367.0ms

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)) 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))))
7.6b
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (real->posit16 1.0) (real->posit16 1.0))
8.7b
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha)

rewrite58.0ms

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:
36.0ms
(/.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))))
8.0ms
(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)

simplify1.3s

Counts
94 → 94
Iterations
IterNodes
done5035
31302
2271
174
039

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize485.0ms

Local error

Found 4 expressions with local error:

0.3b
(*.p16 (/.p16 (real->posit16 1.0) (+.p16 beta (+.p16 alpha (*.p16 (real->posit16 2) (real->posit16 1))))) (/.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 beta (+.p16 alpha (*.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 beta (+.p16 alpha (*.p16 (real->posit16 2) (real->posit16 1)))))
7.6b
(quire16-mul-add (quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha) (real->posit16 1.0) (real->posit16 1.0))
8.7b
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) beta alpha)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
27×p16-times-frac
24×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
13×associate-*r* associate-*l*
6×/p16-rgt-identity-expand
4×+p16-lft-identity-expand +p16-rgt-identity-expand
3×associate-/r* associate-/r/ associate-/l*
2×distribute-rgt-in distribute-lft-in introduce-quire -p16-rgt-identity-expand
1×associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 66
Calls
4 calls:
12.0ms
(*.p16 (/.p16 (real->posit16 1.0) (+.p16 beta (+.p16 alpha (*.p16 (real->posit16 2) (real->posit16 1))))) (/.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 beta (+.p16 alpha (*.p16 (real->posit16 2) (real->posit16 1))))))
10.0ms
(/.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 beta (+.p16 alpha (*.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 (real->posit16 1.0) (+.p16 beta (+.p16 alpha (*.p16 (real->posit16 2) (real->posit16 1))))) (/.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 beta (+.p16 alpha (*.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 beta (+.p16 alpha (*.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)

simplify4.0s

Counts
70 → 70
Iterations
IterNodes
done5003
54543
41218
3582
2227
195
041

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes405.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done24
124
022

end0.0ms

sample6.5s

Algorithm
halfpoints