Details

Time bar (total: 16.2s)

sample100.0ms

Algorithm
halfpoints

simplify16.0ms

Counts
1 → 1
Iterations
IterNodes
done15
215
114
09

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize149.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt.p16 (+.p16 x (real->posit16 1)))
0.1b
(/.p16 (real->posit16 1) (sqrt.p16 x))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.3b
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
77×p16-times-frac
71×*p16-lft-identity-expand p16-*-un-lft-identity
51×*p16-rgt-identity-expand
24×distribute-lft-out--
18×introduce-quire
13×/p16-rgt-identity-expand insert-quire-fdp-sub
9×distribute-rgt-out--
7×associate-/r/
6×associate-/r* +p16-lft-identity-expand -p16-rgt-identity-expand +p16-rgt-identity-expand associate-/l*
2×associate--l+ associate--r+ associate-/l/
1×associate--l- insert-quire-sub sub-neg p16-flip-- associate--r-
Counts
4 → 121
Calls
4 calls:
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))
4.0ms
(/.p16 (real->posit16 1) (sqrt.p16 x))
4.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
31.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

series0.0ms

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

simplify1.5s

Counts
125 → 125
Iterations
IterNodes
done5027
31366
2269
168
042

prune829.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize250.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.3b
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.3b
(-.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
36×p16-times-frac
34×*p16-lft-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
13×associate-*r* associate-*l*
12×+p16-lft-identity-expand +p16-rgt-identity-expand
10×/p16-rgt-identity-expand
6×distribute-rgt-in associate-/r* distribute-lft-in introduce-quire -p16-rgt-identity-expand associate--l+ associate-/l* associate--r+
4×associate-/r/
2×associate-/l/
1×associate--l- insert-quire-sub sub-neg associate-*l/ associate-*r/ p16-flip-- *-commutative insert-quire-fdp-sub associate--r- difference-of-squares
Counts
4 → 118
Calls
4 calls:
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
5.0ms
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
6.0ms
(-.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))

series0.0ms

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

simplify5.7s

Counts
122 → 122
Iterations
IterNodes
done5041
33946
2550
1141
055

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize209.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.3b
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
86×p16-times-frac
79×*p16-lft-identity-expand p16-*-un-lft-identity
59×*p16-rgt-identity-expand
24×distribute-lft-out--
18×introduce-quire
15×/p16-rgt-identity-expand
13×insert-quire-fdp-sub
9×associate-/r* distribute-rgt-out-- associate-/l*
8×associate-/r/
6×+p16-lft-identity-expand -p16-rgt-identity-expand +p16-rgt-identity-expand
3×associate-/l/
2×associate--l+ associate--r+
1×associate--l- insert-quire-sub sub-neg p16-flip-- associate--r-
Counts
4 → 138
Calls
4 calls:
4.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
17.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

series0.0ms

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

simplify1.7s

Counts
142 → 142
Iterations
IterNodes
done5019
31329
2239
163
038

prune895.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

localize281.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
11.1b
(quire16-mul-sub (posit16->quire16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
27×*p16-lft-identity-expand p16-times-frac *p16-rgt-identity-expand p16-*-un-lft-identity
9×associate-/r* /p16-rgt-identity-expand associate-/l*
3×+p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand associate-/r/ +p16-rgt-identity-expand associate-/l/
Counts
4 → 75
Calls
4 calls:
4.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
3.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(quire16-mul-sub (posit16->quire16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(quire16-mul-sub (posit16->quire16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

simplify492.0ms

Counts
79 → 79
Iterations
IterNodes
done515
7515
6471
5377
4296
3191
280
130
022

prune766.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.4b

regimes116.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 0.6b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done11
111
09

end0.0ms

sample2.0s

Algorithm
halfpoints