Details

Time bar (total: 1.8m)

sample1.5s

Algorithm
halfpoints

simplify5.7s

Counts
1 → 1
Iterations
IterNodes
415340
31591
2264
160
019

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize370.0ms

Local error

Found 4 expressions with local error:

0.1b
(*.p16 i (+.p16 (+.p16 alpha beta) 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))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
58×p16-times-frac
37×/p16-rgt-identity-expand
29×*p16-lft-identity-expand associate-/r/ *p16-rgt-identity-expand p16-*-un-lft-identity
24×difference-of-squares
12×associate-*r/
11×associate-*l/
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*
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 → 126
Calls
4 calls:
16.0ms
(*.p16 i (+.p16 (+.p16 alpha beta) i))
6.0ms
(+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i)))
16.0ms
(/.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)))
6.0ms
(/.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 i (+.p16 (+.p16 alpha beta) 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))))

simplify3.6s

Counts
130 → 130
Iterations
IterNodes
37666
2822
1160
065

prune7.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.8b

localize410.0ms

Local error

Found 4 expressions with local error:

0.6b
(/.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)))
0.6b
(/.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)))
1.2b
(/.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)))

rewrite250.0ms

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:
90.0ms
(/.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)))
99.0ms
(/.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)))
24.0ms
(/.p16 (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
27.0ms
(/.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 (*.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 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)))

simplify4.9s

Counts
408 → 408
Iterations
IterNodes
37575
2923
1167
071

prune20.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.5b

localize427.0ms

Local error

Found 4 expressions with local error:

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

rewrite232.0ms

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:
88.0ms
(/.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)))
105.0ms
(/.p16 (*.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 beta i) alpha)) (+.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)))
22.0ms
(/.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 (*.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 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 beta i) alpha)) (+.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)))

simplify4.2s

Counts
284 → 284
Iterations
IterNodes
36320
2913
1158
063

prune14.6s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 0.4b

localize486.0ms

Local error

Found 4 expressions with local error:

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

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
51×*p16-lft-identity-expand p16-*-un-lft-identity
47×*p16-rgt-identity-expand
46×p16-times-frac
25×associate-/r*
13×associate-*r* associate-*l*
12×p16-distribute-lft-out /p16-rgt-identity-expand distribute-lft-out
6×+p16-lft-identity-expand distribute-rgt-out +p16-rgt-identity-expand
5×associate-/r/
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×*-commutative
Counts
4 → 129
Calls
4 calls:
81.0ms
(/.p16 (*.p16 (/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 beta i) alpha)) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
35.0ms
(*.p16 (/.p16 (+.p16 (*.p16 alpha beta) (*.p16 (+.p16 (+.p16 alpha beta) i) i)) (+.p16 (+.p16 (*.p16 i (real->posit16 2)) alpha) beta)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha (-.p16 (*.p16 i (real->posit16 2)) (real->posit16 1.0))) beta)))
13.0ms
(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
21.0ms
(/.p16 (+.p16 (*.p16 alpha beta) (*.p16 (+.p16 (+.p16 alpha beta) i) i)) (+.p16 (+.p16 (*.p16 i (real->posit16 2)) 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 (+.p16 beta i) alpha)) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.0ms
(*.p16 (/.p16 (+.p16 (*.p16 alpha beta) (*.p16 (+.p16 (+.p16 alpha beta) i) i)) (+.p16 (+.p16 (*.p16 i (real->posit16 2)) alpha) beta)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha (-.p16 (*.p16 i (real->posit16 2)) (real->posit16 1.0))) beta)))
0.0ms
(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
0.0ms
(/.p16 (+.p16 (*.p16 alpha beta) (*.p16 (+.p16 (+.p16 alpha beta) i) i)) (+.p16 (+.p16 (*.p16 i (real->posit16 2)) alpha) beta))

simplify2.0s

Counts
133 → 133
Iterations
IterNodes
33540
2688
1155
061

prune8.2s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 0.3b

regimes2.1s

Accuracy

0% (1.0b remaining)

Error of 1.5b against oracle of 0.4b and baseline of 1.5b

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
132
032

end0.0ms

sample28.4s

Algorithm
halfpoints