Details

Time bar (total: 56.0s)

sample1.7s

Algorithm
halfpoints

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5014
31591
2264
160
019

prune79.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.9b

localize426.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
0.2b
(+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i)))
1.3b
(/.p16 (/.p16 (*.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i)))) (*.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))) (-.p16 (*.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (real->posit16 1.0)))
3.1b
(/.p16 (*.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i)))) (*.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
58×p16-times-frac
38×/p16-rgt-identity-expand
30×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
29×associate-/r/
24×difference-of-squares
12×associate-*l/ associate-*r/
8×associate-/r* difference-of-sqr-1 associate-/l*
6×+p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand +p16-rgt-identity-expand
5×associate-/l/
4×associate-+r+
3×associate-*r* associate-*l*
2×distribute-rgt-in associate-+l+ distribute-lft-in
1×+-commutative associate-+r- insert-quire-add p16-flip-- *-commutative insert-quire-fdp-add associate-+l-
Counts
4 → 130
Calls
4 calls:
20.0ms
(*.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
8.0ms
(+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i)))
21.0ms
(/.p16 (/.p16 (*.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i)))) (*.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))) (-.p16 (*.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (real->posit16 1.0)))
14.0ms
(/.p16 (*.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i)))) (*.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))

series0.0ms

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

simplify1.6s

Counts
134 → 134
Iterations
IterNodes
done5000
21070
1192
069

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.7b

localize417.0ms

Local error

Found 4 expressions with local error:

0.6b
(/.p16 (/.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.7b
(/.p16 (/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
1.2b
(/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.2b
(/.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite311.0ms

Algorithm
rewrite-expression-head
Rules
478×p16-times-frac
339×*p16-lft-identity-expand p16-*-un-lft-identity
323×*p16-rgt-identity-expand
84×distribute-lft-out--
48×p16-distribute-lft-out distribute-lft-out
44×/p16-rgt-identity-expand
42×distribute-rgt-out--
38×associate-/r/
37×associate-/r*
24×distribute-rgt-out associate-/l*
8×distribute-lft1-in
5×associate-/l/
4×+p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand +p16-rgt-identity-expand
1×associate-*r/ p16-flip--
Counts
4 → 404
Calls
4 calls:
166.0ms
(/.p16 (/.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
78.0ms
(/.p16 (/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
15.0ms
(/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
16.0ms
(/.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

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

simplify1.8s

Counts
408 → 408
Iterations
IterNodes
done5000
2997
1166
071

prune2.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.4b

localize427.0ms

Local error

Found 4 expressions with local error:

0.6b
(/.p16 (*.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 alpha (+.p16 beta i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.7b
(/.p16 (/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.8b
(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.2b
(/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite311.0ms

Algorithm
rewrite-expression-head
Rules
301×p16-times-frac
226×*p16-lft-identity-expand p16-*-un-lft-identity
222×*p16-rgt-identity-expand
84×distribute-lft-out--
42×distribute-rgt-out--
37×associate-/r*
24×/p16-rgt-identity-expand
18×associate-/r/
17×associate-/l*
12×p16-distribute-lft-out distribute-lft-out
6×distribute-rgt-out
5×associate-/l/
4×+p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand +p16-rgt-identity-expand
2×distribute-lft1-in
1×associate-*l/ associate-*r/ p16-flip--
Counts
4 → 280
Calls
4 calls:
117.0ms
(/.p16 (*.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 alpha (+.p16 beta i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
140.0ms
(/.p16 (/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
16.0ms
(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
28.0ms
(/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

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

simplify1.6s

Counts
284 → 284
Iterations
IterNodes
done5000
2982
1155
063

prune2.0s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 0.3b

localize587.0ms

Local error

Found 4 expressions with local error:

0.6b
(/.p16 (*.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 alpha (+.p16 beta i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.8b
(*.p16 (/.p16 (+.p16 (*.p16 alpha beta) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta))) (/.p16 (real->posit16 1.0) (-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0))))
0.8b
(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.2b
(/.p16 (+.p16 (*.p16 alpha beta) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta)))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
78×*p16-lft-identity-expand p16-*-un-lft-identity
74×*p16-rgt-identity-expand
73×p16-times-frac
41×associate-*r*
25×associate-/r*
18×distribute-lft-out--
13×associate-*l*
12×p16-distribute-lft-out /p16-rgt-identity-expand distribute-lft-out
9×distribute-rgt-out--
6×+p16-lft-identity-expand distribute-rgt-out associate-/r/ +p16-rgt-identity-expand
4×introduce-quire -p16-rgt-identity-expand associate-/l* associate-/l/
2×distribute-rgt-in distribute-lft-in distribute-lft1-in associate-*l/ associate-*r/
1×p16-flip-- *-commutative
Counts
4 → 157
Calls
4 calls:
107.0ms
(/.p16 (*.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 alpha (+.p16 beta i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
49.0ms
(*.p16 (/.p16 (+.p16 (*.p16 alpha beta) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta))) (/.p16 (real->posit16 1.0) (-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0))))
12.0ms
(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
27.0ms
(/.p16 (+.p16 (*.p16 alpha beta) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta)))

series0.0ms

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

simplify2.7s

Counts
161 → 161
Iterations
IterNodes
done5000
21001
1172
062

prune1.7s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 0.3b

regimes2.6s

Accuracy

0% (0.9b remaining)

Error of 1.4b against oracle of 0.4b and baseline of 1.4b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done29
029

end0.0ms

sample31.9s

Algorithm
halfpoints