Details

Time bar (total: 13.8s)

sample113.0ms

Algorithm
halfpoints

simplify33.0ms

Counts
1 → 1
Iterations
IterNodes
done15
215
114
09

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize244.0ms

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))))
0.5b
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

rewrite20.0ms

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)))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 x))
3.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
11.0ms
(-.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
done2034
42034
31366
2269
168
042

prune759.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize330.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b
(/.p16 (-.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)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.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)))))
0.4b
(-.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))))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
717×p16-times-frac
512×*p16-lft-identity-expand p16-*-un-lft-identity
252×*p16-rgt-identity-expand
120×p16-distribute-lft-out distribute-lft-out
63×associate-/r*
62×difference-of-squares
45×distribute-rgt-out
30×/p16-rgt-identity-expand
24×associate-/r/
13×associate-*r* associate-*l*
12×+p16-lft-identity-expand +p16-rgt-identity-expand
7×associate-/l*
6×distribute-rgt-in distribute-lft-in introduce-quire -p16-rgt-identity-expand associate--l+ associate--r+
3×associate-/l/
2×p16-flip--
1×associate--l- insert-quire-sub sub-neg associate-*l/ associate-*r/ *-commutative insert-quire-fdp-sub associate--r-
Counts
4 → 408
Calls
4 calls:
3.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
30.0ms
(/.p16 (-.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)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.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 (-.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)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.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))))))

simplify1.2s

Counts
412 → 412
Iterations
IterNodes
done2024
32024
2837
1175
078

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize354.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.5b
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))))

rewrite24.0ms

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:
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
12.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))))

series0.0ms

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

simplify1.4s

Counts
142 → 142
Iterations
IterNodes
done2025
42025
31469
2269
170
041

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize286.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.3b
(*.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 1) (sqrt.p16 x))) (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))))) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 1) (sqrt.p16 x)))))
0.5b
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
527×p16-times-frac
387×*p16-lft-identity-expand p16-*-un-lft-identity
211×*p16-rgt-identity-expand
184×associate-*r*
72×p16-distribute-lft-out distribute-lft-out
29×/p16-rgt-identity-expand
27×distribute-rgt-out
24×distribute-lft-out--
20×associate-/r/
18×introduce-quire
13×insert-quire-fdp-sub
9×distribute-rgt-out--
8×+p16-lft-identity-expand +p16-rgt-identity-expand
6×associate-/r* -p16-rgt-identity-expand associate-/l*
5×associate-*l/
3×associate-*r/
2×distribute-rgt-in distribute-lft-in associate--l+ p16-flip-- associate--r+ associate-/l/
1×associate--l- insert-quire-sub sub-neg associate-*l* *-commutative associate--r-
Counts
4 → 316
Calls
4 calls:
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
13.0ms
(*.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 1) (sqrt.p16 x))) (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))))) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 1) (sqrt.p16 x)))))
12.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.0ms
(*.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 1) (sqrt.p16 x))) (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))))) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))) (/.p16 (real->posit16 1) (sqrt.p16 x)))))
0.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))))

simplify1.6s

Counts
320 → 320
Iterations
IterNodes
done2001
32001
2519
1116
055

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.4b

regimes221.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done14
114
012

end0.0ms

sample1.7s

Algorithm
halfpoints