Details

Time bar (total: 1.1m)

sample789.0ms

Algorithm
halfpoints

simplify737.0ms

Counts
1 → 1
Iterations
IterNodes
42074
3418
293
135
019

prune88.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize342.0ms

Local error

Found 4 expressions with local error:

0.1b
(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.3b
(+.p16 (/.p16 (/.p16 (*.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0))) (real->posit16 1.0))
0.6b
(/.p16 (/.p16 (*.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
0.7b
(/.p16 (*.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite436.0ms

Algorithm
rewrite-expression-head
Rules
126×p16-times-frac
117×*p16-lft-identity-expand p16-*-un-lft-identity
67×*p16-rgt-identity-expand
38×p16-distribute-lft-out distribute-lft-out
26×/p16-rgt-identity-expand
19×associate-/r/
15×associate-/r*
14×distribute-rgt-out
10×introduce-quire
8×-p16-rgt-identity-expand associate-/l*
7×+p16-lft-identity-expand +p16-rgt-identity-expand
5×associate-/l/
4×associate-+r+ insert-quire-fdp-add
3×associate-+l+
2×+-commutative associate-+r- insert-quire-add distribute-lft1-in associate-*r/ associate-+l-
1×associate-*l/ p16-flip--
Counts
4 → 188
Calls
4 calls:
8.0ms
(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
253.0ms
(+.p16 (/.p16 (/.p16 (*.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0))) (real->posit16 1.0))
143.0ms
(/.p16 (/.p16 (*.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
28.0ms
(/.p16 (*.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.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 (/.p16 (*.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0))) (real->posit16 1.0))
0.0ms
(/.p16 (/.p16 (*.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
0.0ms
(/.p16 (*.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify1.7s

Counts
192 → 192
Iterations
IterNodes
33161
2460
1118
060

prune9.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize747.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.p16 (/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha)))) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2))))))
0.3b
(+.p16 (*.p16 (/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha)))) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))) (real->posit16 1.0))
0.6b
(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))
0.6b
(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
36×p16-times-frac
35×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
13×associate-*r* associate-*l*
10×+p16-lft-identity-expand /p16-rgt-identity-expand +p16-rgt-identity-expand
8×introduce-quire
6×associate-+l+ associate-/r* -p16-rgt-identity-expand associate-/l*
4×distribute-rgt-in distribute-lft-in associate-/r/
3×insert-quire-fdp-add associate-/l/
2×associate-+r+
1×+-commutative associate-+r- insert-quire-add associate-*l/ associate-*r/ p16-flip-- *-commutative associate-+l-
Counts
4 → 115
Calls
4 calls:
58.0ms
(*.p16 (/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha)))) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2))))))
8.0ms
(+.p16 (*.p16 (/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha)))) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))) (real->posit16 1.0))
17.0ms
(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))
91.0ms
(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(*.p16 (/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha)))) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2))))))
0.0ms
(+.p16 (*.p16 (/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha)))) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))) (real->posit16 1.0))
0.0ms
(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))
0.0ms
(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))))

simplify1.8s

Counts
119 → 119
Iterations
IterNodes
33431
2831
1135
059

prune5.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize448.0ms

Local error

Found 4 expressions with local error:

0.3b
(+.p16 (*.p16 (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))) (+.p16 beta alpha))) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))) (real->posit16 1.0))
0.3b
(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))) (+.p16 beta alpha)))
0.5b
(/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))) (+.p16 beta alpha))
0.6b
(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
93×p16-times-frac
63×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
19×associate-/r*
13×/p16-rgt-identity-expand
9×associate-/l*
8×+p16-lft-identity-expand introduce-quire +p16-rgt-identity-expand
7×associate-/r/
6×associate-+l+ -p16-rgt-identity-expand
4×associate-/l/
3×insert-quire-fdp-add
2×distribute-rgt-in associate-+r+ distribute-lft-in
1×+-commutative associate-+r- insert-quire-add p16-flip-- associate-+l-
Counts
4 → 139
Calls
4 calls:
3.0ms
(+.p16 (*.p16 (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))) (+.p16 beta alpha))) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))) (real->posit16 1.0))
82.0ms
(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))) (+.p16 beta alpha)))
106.0ms
(/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))) (+.p16 beta alpha))
12.0ms
(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(+.p16 (*.p16 (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))) (+.p16 beta alpha))) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))) (real->posit16 1.0))
0.0ms
(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))) (+.p16 beta alpha)))
0.0ms
(/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))) (+.p16 beta alpha))
0.0ms
(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))

simplify6.6s

Counts
143 → 143
Iterations
IterNodes
410621
31826
2347
1111
056

prune7.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize435.0ms

Local error

Found 4 expressions with local error:

0.3b
(+.p16 (/.p16 (*.p16 (+.p16 beta alpha) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha)))) (real->posit16 1.0))
0.3b
(*.p16 (+.p16 beta alpha) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2))))))
0.6b
(/.p16 (*.p16 (+.p16 beta alpha) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))))
0.6b
(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
35×*p16-lft-identity-expand p16-*-un-lft-identity
33×*p16-rgt-identity-expand
21×p16-times-frac
15×/p16-rgt-identity-expand
13×associate-*r*
8×+p16-lft-identity-expand introduce-quire +p16-rgt-identity-expand
7×associate-/r/
6×associate-/r* p16-distribute-lft-out distribute-rgt-out -p16-rgt-identity-expand distribute-lft-out
5×associate-/l/
4×associate-/l*
3×associate-*l* insert-quire-fdp-add
2×distribute-rgt-in associate-+l+ associate-+r+ distribute-lft-in distribute-lft1-in associate-*l/ associate-*r/
1×+-commutative associate-+r- insert-quire-add p16-flip-- *-commutative associate-+l-
Counts
4 → 115
Calls
4 calls:
178.0ms
(+.p16 (/.p16 (*.p16 (+.p16 beta alpha) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha)))) (real->posit16 1.0))
6.0ms
(*.p16 (+.p16 beta alpha) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2))))))
78.0ms
(/.p16 (*.p16 (+.p16 beta alpha) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))))
25.0ms
(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(+.p16 (/.p16 (*.p16 (+.p16 beta alpha) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha)))) (real->posit16 1.0))
0.0ms
(*.p16 (+.p16 beta alpha) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2))))))
0.0ms
(/.p16 (*.p16 (+.p16 beta alpha) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))))
0.0ms
(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))

simplify7.8s

Counts
119 → 119
Iterations
IterNodes
35991
2550
1127
054

prune5.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

regimes867.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
123
023

end0.0ms

sample14.1s

Algorithm
halfpoints