Details

Time bar (total: 16.9s)

sample80.0ms

Algorithm
halfpoints

simplify7.0ms

Counts
1 → 1
Iterations
IterNodes
done13
213
112
07

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize90.0ms

Local error

Found 2 expressions with local error:

0.1b
(sqrt.p16 (+.p16 x (real->posit16 1)))
0.9b
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
7×*p16-lft-identity-expand p16-*-un-lft-identity
6×introduce-quire
5×*p16-rgt-identity-expand
4×+p16-lft-identity-expand -p16-rgt-identity-expand +p16-rgt-identity-expand distribute-lft-out--
3×insert-quire-fdp-sub
2×associate--l+ /p16-rgt-identity-expand associate--r+
1×associate--l- insert-quire-sub sub-neg distribute-rgt-out-- p16-flip-- associate--r-
Counts
2 → 33
Calls
2 calls:
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))
3.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

series0.0ms

Counts
2 → 2
Calls
2 calls:
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))
0.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

simplify1.1s

Counts
35 → 35
Iterations
IterNodes
done5002
3834
2126
137
023

prune278.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.9b

localize149.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt.p16 (+.p16 (real->posit16 1) x))
0.1b
(/.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.2b
(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.9b
(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
41×*p16-lft-identity-expand p16-*-un-lft-identity
19×*p16-rgt-identity-expand
12×associate-/r* p16-distribute-lft-out p16-times-frac associate-*l* distribute-lft-out
10×+p16-lft-identity-expand /p16-rgt-identity-expand +p16-rgt-identity-expand
8×introduce-quire associate-*r* -p16-rgt-identity-expand distribute-lft-out--
6×distribute-rgt-in distribute-lft-in associate--l+
4×associate-*r/ associate-/l/
3×sub-neg distribute-rgt-out p16-flip-- insert-quire-fdp-sub associate--r-
2×distribute-rgt-out-- associate-*l/ associate--r+
1×associate--l- insert-quire-sub associate-/r/ *-commutative associate-/l*
Counts
4 → 115
Calls
4 calls:
0.0ms
(sqrt.p16 (+.p16 (real->posit16 1) x))
9.0ms
(/.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
12.0ms
(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
14.0ms
(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(sqrt.p16 (+.p16 (real->posit16 1) x))
0.0ms
(/.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.0ms
(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.0ms
(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

simplify1.8s

Counts
119 → 119
Iterations
IterNodes
done5001
2787
1108
046

prune778.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize240.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt.p16 (+.p16 (real->posit16 1) x))
0.1b
(sqrt.p16 (+.p16 (real->posit16 1) x))
0.1b
(/.p16 (+.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (neg.p16 (sqrt.p16 x)))) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.4b
(+.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (neg.p16 (sqrt.p16 x))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
71×*p16-lft-identity-expand p16-*-un-lft-identity
60×p16-times-frac
38×p16-distribute-lft-out distribute-lft-out
35×*p16-rgt-identity-expand
12×associate-/r*
10×+p16-lft-identity-expand +p16-rgt-identity-expand
6×associate-+l+ associate-+r+ distribute-rgt-out introduce-quire -p16-rgt-identity-expand /p16-rgt-identity-expand
5×associate-/l*
4×distribute-rgt-in distribute-lft-in
1×+-commutative associate-+r- insert-quire-add associate-/r/ insert-quire-fdp-add associate-+l- associate-/l/
Counts
4 → 130
Calls
4 calls:
0.0ms
(sqrt.p16 (+.p16 (real->posit16 1) x))
0.0ms
(sqrt.p16 (+.p16 (real->posit16 1) x))
5.0ms
(/.p16 (+.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (neg.p16 (sqrt.p16 x)))) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
4.0ms
(+.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (neg.p16 (sqrt.p16 x))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(sqrt.p16 (+.p16 (real->posit16 1) x))
0.0ms
(sqrt.p16 (+.p16 (real->posit16 1) x))
0.0ms
(/.p16 (+.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (neg.p16 (sqrt.p16 x)))) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.0ms
(+.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (neg.p16 (sqrt.p16 x))))

simplify4.2s

Counts
134 → 134
Iterations
IterNodes
done5012
31716
2231
192
046

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize233.0ms

Local error

Found 4 expressions with local error:

0.1b
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
0.3b
(/.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))))
0.3b
(*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.3b
(-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
14×+p16-lft-identity-expand /p16-rgt-identity-expand +p16-rgt-identity-expand
8×distribute-rgt-in *p16-lft-identity-expand distribute-lft-in *p16-rgt-identity-expand p16-*-un-lft-identity
6×introduce-quire associate-*r* associate-*l* -p16-rgt-identity-expand associate--l+ associate--r+
5×associate-*r/
4×associate-*l/ associate-/l/
3×associate-/r/
2×p16-flip-- *-commutative sqrt-sqrd.p16
1×associate--l- insert-quire-sub associate-/r* sub-neg p16-times-frac insert-quire-fdp-sub associate-/l* associate--r- difference-of-squares
Counts
4 → 89
Calls
4 calls:
4.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
8.0ms
(/.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))))
4.0ms
(*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x)))
4.0ms
(-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
0.0ms
(/.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))))
0.0ms
(*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.0ms
(-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))

simplify4.1s

Counts
93 → 93
Iterations
IterNodes
done5003
33641
2615
1113
050

prune853.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

regimes179.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done14
114
012

end0.0ms

sample1.7s

Algorithm
halfpoints