Details

Time bar (total: 10.1s)

sample91.0ms

Algorithm
halfpoints

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done13
213
112
07

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize114.0ms

Local error

Found 2 expressions with local error:

0.1b
(sqrt.p16 (+.p16 x (real->posit16 1)))
0.8b
(-.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)))
2.0ms
(-.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))

simplify950.0ms

Counts
35 → 35
Iterations
IterNodes
done2003
42003
3834
2126
137
023

prune278.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize229.0ms

Local error

Found 4 expressions with local error:

0.1b
(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.2b
(/.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)))
0.8b
(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
50×*p16-lft-identity-expand p16-*-un-lft-identity
22×*p16-rgt-identity-expand
16×p16-distribute-lft-out distribute-lft-out
12×associate-/r* +p16-lft-identity-expand introduce-quire p16-times-frac associate-*l* +p16-rgt-identity-expand
10×-p16-rgt-identity-expand /p16-rgt-identity-expand
8×associate-*r* distribute-lft-out--
6×distribute-rgt-in distribute-lft-in associate--l+
4×distribute-rgt-out associate-*r/ associate-/l/
3×sub-neg p16-flip-- insert-quire-fdp-add insert-quire-fdp-sub associate--r-
2×associate-+l+ associate-+r+ distribute-rgt-out-- associate-*l/ associate--r+
1×associate--l- +-commutative insert-quire-sub associate-+r- insert-quire-add associate-/r/ *-commutative associate-+l- associate-/l*
Counts
4 → 135
Calls
4 calls:
6.0ms
(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
12.0ms
(/.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)))
11.0ms
(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
5.0ms
(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(+.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)) (-.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))

simplify841.0ms

Counts
139 → 139
Iterations
IterNodes
done2000
32000
2723
1113
050

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize348.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
24×*p16-lft-identity-expand p16-*-un-lft-identity
15×associate-*r* associate-*l*
14×/p16-rgt-identity-expand
12×+p16-lft-identity-expand *p16-rgt-identity-expand +p16-rgt-identity-expand
8×p16-distribute-lft-out distribute-lft-out
7×distribute-rgt-in distribute-lft-in
6×introduce-quire -p16-rgt-identity-expand associate--l+ associate--r+
5×associate-*r/
4×associate-*l/ associate-/l/
3×associate-/r/
2×distribute-rgt-out p16-flip-- *-commutative
1×associate--l- insert-quire-sub associate-/r* sub-neg p16-times-frac sqrt-sqrd.p16 insert-quire-fdp-sub associate-/l* associate--r- difference-of-squares
Counts
4 → 104
Calls
4 calls:
11.0ms
(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
7.0ms
(-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.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)))

series0.0ms

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

simplify939.0ms

Counts
108 → 108
Iterations
IterNodes
done2008
32008
2685
1132
054

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize210.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
24×*p16-lft-identity-expand p16-*-un-lft-identity
15×associate-*r* associate-*l*
14×/p16-rgt-identity-expand
12×*p16-rgt-identity-expand
9×+p16-lft-identity-expand +p16-rgt-identity-expand
8×p16-distribute-lft-out introduce-quire distribute-lft-out
7×-p16-rgt-identity-expand
6×associate--r+
5×distribute-rgt-in distribute-lft-in associate-*r/
4×associate-*l/ associate-/l/
3×associate-/r/
2×associate--l- insert-quire-sub insert-quire-add distribute-rgt-out p16-flip-- *-commutative insert-quire-fdp-sub
1×associate-/r* sub-neg p16-times-frac associate--l+ associate-+l- sqrt-sqrd.p16 associate-/l* associate--r-
Counts
4 → 101
Calls
4 calls:
4.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
10.0ms
(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
18.0ms
(-.p16 (+.p16 (real->posit16 1) x) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
8.0ms
(/.p16 (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.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))))

series0.0ms

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

simplify794.0ms

Counts
105 → 105
Iterations
IterNodes
done2003
32003
2918
1142
055

prune776.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes194.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done19
119
017

end0.0ms

sample2.0s

Algorithm
halfpoints