Details

Time bar (total: 53.5s)

sample1.4s

Algorithm
halfpoints

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5001
31775
2279
160
019

prune69.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize409.0ms

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)))
1.4b
(/.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))))

rewrite36.0ms

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:
8.0ms
(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
3.0ms
(+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i)))
11.0ms
(/.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)))
12.0ms
(/.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))))

simplify1.6s

Counts
131 → 131
Iterations
IterNodes
done5000
21217
1173
069

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.7b

localize429.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.p16 (/.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))
1.3b
(/.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)))
1.4b
(/.p16 (*.p16 (/.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) 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)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
31×p16-times-frac
27×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
13×associate-/r* associate-*r* /p16-rgt-identity-expand
7×associate-*l*
6×+p16-lft-identity-expand associate-/r/ +p16-rgt-identity-expand difference-of-squares associate-/l/
5×associate-/l*
4×introduce-quire -p16-rgt-identity-expand
3×associate-*r/
2×distribute-rgt-in distribute-lft-in difference-of-sqr-1 associate-*l/
1×p16-flip-- *-commutative
Counts
4 → 106
Calls
4 calls:
33.0ms
(*.p16 (/.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))
26.0ms
(/.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
23.0ms
(/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
8.0ms
(/.p16 (*.p16 (/.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) 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)))

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

simplify1.8s

Counts
110 → 110
Iterations
IterNodes
done5001
21933
1191
067

prune2.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.6b

localize550.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.p16 (/.p16 i (/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) i))) (/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))
1.1b
(/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) i))
1.4b
(/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.4b
(/.p16 (*.p16 (/.p16 i (/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) i))) (/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) 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)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
34×p16-times-frac
32×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
13×associate-/r* associate-*r*
11×/p16-rgt-identity-expand
7×associate-/l*
6×+p16-lft-identity-expand associate-/r/ +p16-rgt-identity-expand difference-of-squares
5×associate-/l/
4×introduce-quire associate-*l* -p16-rgt-identity-expand
2×distribute-rgt-in distribute-lft-in difference-of-sqr-1 associate-*l/ associate-*r/
1×p16-flip-- *-commutative
Counts
4 → 110
Calls
4 calls:
16.0ms
(*.p16 (/.p16 i (/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) i))) (/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))
53.0ms
(/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) i))
22.0ms
(/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
9.0ms
(/.p16 (*.p16 (/.p16 i (/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) i))) (/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) 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)))

series0.0ms

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

simplify1.9s

Counts
114 → 114
Iterations
IterNodes
done5000
21686
1187
066

prune2.9s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 0.5b

localize415.0ms

Local error

Found 4 expressions with local error:

0.6b
(*.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (*.p16 (/.p16 (+.p16 alpha (+.p16 beta i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (*.p16 i (+.p16 alpha (+.p16 beta i))) (*.p16 beta alpha))))
0.9b
(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.1b
(/.p16 (+.p16 alpha (+.p16 beta i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.4b
(/.p16 (*.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (*.p16 (/.p16 (+.p16 alpha (+.p16 beta i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (*.p16 i (+.p16 alpha (+.p16 beta i))) (*.p16 beta alpha)))) (-.p16 (*.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (real->posit16 1.0)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
18×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
16×p16-times-frac
14×/p16-rgt-identity-expand
13×associate-/r*
8×associate-*r/
6×distribute-rgt-in distribute-lft-in +p16-lft-identity-expand +p16-rgt-identity-expand difference-of-squares associate-/l/
5×associate-/r/
4×introduce-quire associate-*l* -p16-rgt-identity-expand associate-*l/ associate-/l*
2×difference-of-sqr-1
1×associate-*r* p16-flip-- *-commutative
Counts
4 → 93
Calls
4 calls:
17.0ms
(*.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (*.p16 (/.p16 (+.p16 alpha (+.p16 beta i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (*.p16 i (+.p16 alpha (+.p16 beta i))) (*.p16 beta alpha))))
6.0ms
(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
15.0ms
(/.p16 (+.p16 alpha (+.p16 beta i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
8.0ms
(/.p16 (*.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (*.p16 (/.p16 (+.p16 alpha (+.p16 beta i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (*.p16 i (+.p16 alpha (+.p16 beta i))) (*.p16 beta alpha)))) (-.p16 (*.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (real->posit16 1.0)))

series0.0ms

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

simplify1.7s

Counts
97 → 97
Iterations
IterNodes
done5001
21630
1232
072

prune1.6s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 0.4b

regimes2.1s

Accuracy

0% (1.1b remaining)

Error of 1.6b against oracle of 0.5b and baseline of 1.6b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done24
024

end0.0ms

sample30.0s

Algorithm
halfpoints