Details

Time bar (total: 56.3s)

sample1.5s

Algorithm
halfpoints

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done5014
31591
2264
160
019

prune57.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.2b

localize383.0ms

Local error

Found 4 expressions with local error:

0.2b
(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.2b
(+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i)))
1.5b
(/.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)))
3.4b
(/.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))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
58×p16-times-frac
36×/p16-rgt-identity-expand
29×associate-/r/
28×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
24×difference-of-squares
11×associate-*l/ associate-*r/
8×associate-/r* introduce-quire difference-of-sqr-1 -p16-rgt-identity-expand associate-/l*
7×+p16-lft-identity-expand +p16-rgt-identity-expand
6×associate-+r+
5×associate-/l/
3×associate-+l+
2×+-commutative associate-+r- insert-quire-add insert-quire-fdp-add associate-+l-
1×distribute-rgt-in distribute-lft-in p16-flip--
Counts
4 → 127
Calls
4 calls:
17.0ms
(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
7.0ms
(+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i)))
8.0ms
(/.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)))
8.0ms
(/.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 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))))

simplify1.5s

Counts
131 → 131
Iterations
IterNodes
done5008
2937
1172
069

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.8b

localize481.0ms

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)))
1.4b
(/.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.4b
(/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite251.0ms

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:
118.0ms
(/.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)))
79.0ms
(/.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)))
14.0ms
(/.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
26.0ms
(/.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) 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 i (+.p16 (+.p16 alpha beta) 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)))

simplify1.8s

Counts
408 → 408
Iterations
IterNodes
done5007
2947
1167
071

prune2.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.5b

localize476.0ms

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)))
0.9b
(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.4b
(/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite203.0ms

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:
70.0ms
(/.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)))
85.0ms
(/.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)))
13.0ms
(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
27.0ms
(/.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)))

simplify2.1s

Counts
284 → 284
Iterations
IterNodes
done5000
2982
1155
063

prune2.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 0.5b

localize655.0ms

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 (real->posit16 1.0) (-.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta)) (real->posit16 1.0))) (/.p16 (+.p16 (*.p16 alpha beta) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta))))
0.9b
(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.4b
(/.p16 (+.p16 (*.p16 alpha beta) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta)))

rewrite197.0ms

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-*l*
25×associate-/r*
18×distribute-lft-out--
13×associate-*r*
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:
112.0ms
(/.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)))
48.0ms
(*.p16 (/.p16 (real->posit16 1.0) (-.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta)) (real->posit16 1.0))) (/.p16 (+.p16 (*.p16 alpha beta) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta))))
7.0ms
(/.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 (real->posit16 1.0) (-.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta)) (real->posit16 1.0))) (/.p16 (+.p16 (*.p16 alpha beta) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta))))
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)))

simplify3.1s

Counts
161 → 161
Iterations
IterNodes
done5012
34442
2777
1159
059

prune1.8s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 0.4b

regimes2.3s

Accuracy

0% (0.9b remaining)

Error of 1.4b against oracle of 0.5b and baseline of 1.4b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done28
028

end0.0ms

sample31.0s

Algorithm
halfpoints