Details

Time bar (total: 21.5s)

sample79.0ms

Algorithm
halfpoints

simplify11.0ms

Counts
1 → 1
Iterations
IterNodes
done13
213
112
07

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize127.0ms

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))

rewrite7.0ms

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)))
6.0ms
(-.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

prune226.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.9b

localize200.0ms

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))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
452×*p16-lft-identity-expand p16-*-un-lft-identity
300×p16-times-frac
182×*p16-rgt-identity-expand
168×associate-*l*
160×p16-distribute-lft-out distribute-lft-out
112×associate-*r*
60×distribute-lft-out--
40×distribute-rgt-out
25×associate-/l*
15×distribute-rgt-out--
14×*-commutative
12×associate-/r*
10×+p16-lft-identity-expand /p16-rgt-identity-expand +p16-rgt-identity-expand
8×introduce-quire -p16-rgt-identity-expand
6×distribute-rgt-in distribute-lft-in associate--l+
4×associate-*r/ associate-/l/
3×sub-neg p16-flip-- insert-quire-fdp-sub associate--r-
2×associate-*l/ associate--r+
1×associate--l- insert-quire-sub associate-/r/
Counts
4 → 427
Calls
4 calls:
0.0ms
(sqrt.p16 (+.p16 (real->posit16 1) x))
42.0ms
(/.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)))
9.0ms
(*.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 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))

simplify3.5s

Counts
431 → 431
Iterations
IterNodes
done5019
33342
2546
1125
054

prune835.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize197.0ms

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))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
10687×*p16-lft-identity-expand p16-*-un-lft-identity
8132×associate-*l*
6846×p16-distribute-lft-out distribute-lft-out
4344×p16-times-frac
2791×*p16-rgt-identity-expand
1162×distribute-rgt-out
362×associate-/l*
283×associate-*r*
29×*-commutative
25×introduce-quire
20×insert-quire-fdp-add
12×associate-/r*
10×+p16-lft-identity-expand +p16-rgt-identity-expand
6×associate-+l+ associate-+r+ -p16-rgt-identity-expand /p16-rgt-identity-expand
4×distribute-rgt-in distribute-lft-in
1×+-commutative associate-+r- insert-quire-add associate-/r/ associate-+l- associate-/l/
Counts
4 → 5147
Calls
4 calls:
0.0ms
(sqrt.p16 (+.p16 (real->posit16 1) x))
0.0ms
(sqrt.p16 (+.p16 (real->posit16 1) x))
305.0ms
(/.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)))
90.0ms
(+.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))))

simplify4.7s

Counts
5151 → 5151
Iterations
IterNodes
done5002
31416
2358
1120
066

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize274.0ms

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)))

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
1692×*p16-lft-identity-expand p16-*-un-lft-identity
1483×associate-*r*
1405×associate-*l*
1276×p16-times-frac
724×*p16-rgt-identity-expand
496×distribute-lft-out--
480×p16-distribute-lft-out distribute-lft-out
202×*-commutative
124×distribute-rgt-out-- difference-of-squares
120×distribute-rgt-out
44×associate-/l*
29×associate-/r*
16×introduce-quire
14×+p16-lft-identity-expand /p16-rgt-identity-expand +p16-rgt-identity-expand
11×insert-quire-fdp-sub
8×distribute-rgt-in distribute-lft-in
6×-p16-rgt-identity-expand associate--l+ associate--r+
5×associate-*r/
4×associate-*l/ associate-/l/
3×associate-/r/
2×p16-flip-- sqrt-sqrd.p16
1×associate--l- insert-quire-sub sub-neg associate--r-
Counts
4 → 1468
Calls
4 calls:
3.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
106.0ms
(/.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))))
6.0ms
(*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x)))
31.0ms
(-.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)))

simplify3.9s

Counts
1472 → 1472
Iterations
IterNodes
done5001
21048
1217
091

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

regimes196.0ms

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

sample1.6s

Algorithm
halfpoints