Details

Time bar (total: 1.9m)

sample283.0ms

Algorithm
halfpoints

simplify877.0ms

Counts
1 → 1
Iterations
IterNodes
43061
3490
2109
139
018

prune78.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize325.0ms

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))))

rewrite290.0ms

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))
142.0ms
(/.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))
66.0ms
(/.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))))

simplify2.0s

Counts
410 → 410
Iterations
IterNodes
34230
2516
1116
055

prune19.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize411.0ms

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))))
6.6b
(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))
10.5b
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0))

rewrite45.0ms

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:
22.0ms
(/.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))))
21.0ms
(/.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))

simplify6.8s

Counts
94 → 94
Iterations
IterNodes
49911
31800
2317
176
040

prune6.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize484.0ms

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)))))
0.7b
(/.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))))
6.6b
(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))
10.5b
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0))

rewrite26.0ms

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:
13.0ms
(/.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)))))
11.0ms
(/.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))

simplify3.1s

Counts
94 → 94
Iterations
IterNodes
131861
121861
111860
101834
91540
81125
7807
6634
5374
4267
3158
280
154
034

prune6.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize653.0ms

Local error

Found 4 expressions with local error:

0.3b
(/.p16 (/.p16 (/.p16 (real->posit16 1.0) (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (real->posit16 1.0) (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))))
0.6b
(/.p16 (/.p16 (real->posit16 1.0) (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (real->posit16 1.0) (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)))))
6.6b
(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))
10.5b
(quire16-mul-add (posit16->quire16 (+.p16 alpha beta)) (*.p16 beta alpha) (real->posit16 1.0))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
2552×p16-times-frac
1104×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
186×associate-/l*
138×associate-/r/
135×/p16-rgt-identity-expand
16×associate-/r*
2×+p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand +p16-rgt-identity-expand associate-/l/
Counts
4 → 910
Calls
4 calls:
59.0ms
(/.p16 (/.p16 (/.p16 (real->posit16 1.0) (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (real->posit16 1.0) (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))))
23.0ms
(/.p16 (/.p16 (real->posit16 1.0) (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (real->posit16 1.0) (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))
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 (/.p16 (/.p16 (real->posit16 1.0) (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (real->posit16 1.0) (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 (/.p16 (real->posit16 1.0) (+.p16 (*.p16 (real->posit16 1) (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (real->posit16 1.0) (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))

simplify4.2s

Counts
914 → 914
Iterations
IterNodes
47516
31140
2325
1142
072

prune56.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes545.0ms

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
223
123
021

end0.0ms

sample6.3s

Algorithm
halfpoints