Details

sample88.0ms

Algorithm: halfpoints

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize101.0ms

Local error

Found 2 expressions with local error:

0.1b	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.6b	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`p16-lft-identity-expand` `p16--un-lft-identity`
14×	`*p16-rgt-identity-expand`
9×	`p16-times-frac`
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×	`associate-/r` `insert-quire-fdp-sub` `associate-/l`
2×	`distribute-rgt-out--` `associate--l+` `associate-/r/` `associate--r+`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `p16-flip--` `associate--r-` `associate-/l/`

Counts

2 → 51

Calls

2 calls:

3.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
10.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))

series0.0ms

Counts

2 → 2

Calls

2 calls:

0.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))

simplify1.3s

Counts

53 → 53

Iterations

Iter	Nodes
done	2090
4	2090
3	1281
2	237
1	52
0	29

prune464.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize196.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.3b	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.6b	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
0.9b	(/.p16 (*.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

57×	`p16-lft-identity-expand` `p16--un-lft-identity`
36×	`introduce-quire` `*p16-rgt-identity-expand`
31×	`p16-times-frac`
26×	`insert-quire-fdp-add`
16×	`p16-distribute-lft-out` `distribute-lft-out`
15×	`/p16-rgt-identity-expand`
13×	`associate-/r*`
10×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
8×	`distribute-rgt-out` `associate-/r/`
4×	`associate-+l+` `associate-+r+` `distribute-lft-out--` `associate-/l/`
3×	`insert-quire-fdp-sub`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `distribute-rgt-out--` `associate-*l/` `associate--l+` `p16-flip--` `associate-+l-` `associate--r+`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `associate-r/` `associate-/l` `associate--r-`

Counts

4 → 144

Calls

4 calls:

14.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
22.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
19.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
58.0ms	(/.p16 (*.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
0.0ms	(/.p16 (*.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))

simplify1.1s

Counts

148 → 148

Iterations

Iter	Nodes
done	2006
3	2006
2	635
1	92
0	48

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

localize244.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.3b	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.6b	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
0.7b	(/.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

199×	`p16-lft-identity-expand` `p16--un-lft-identity`
135×	`p16-times-frac`
124×	`*p16-rgt-identity-expand`
60×	`distribute-lft-out--`
48×	`p16-distribute-lft-out` `distribute-lft-out`
36×	`introduce-quire`
35×	`/p16-rgt-identity-expand`
30×	`distribute-rgt-out--` `associate-/r/`
26×	`insert-quire-fdp-add`
24×	`distribute-rgt-out`
13×	`associate-/r*`
10×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
9×	`associate-/l*`
4×	`associate-+l+` `associate-+r+`
3×	`insert-quire-fdp-sub`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `associate--l+` `p16-flip--` `associate-+l-` `associate--r+` `associate-/l/`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `associate--r-`

Counts

4 → 254

Calls

4 calls:

15.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
12.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
19.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
73.0ms	(/.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
0.0ms	(/.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))

simplify1.4s

Counts

258 → 258

Iterations

Iter	Nodes
done	2010
3	2010
2	471
1	81
0	46

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize282.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.3b	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.6b	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
0.8b	(*.p16 (/.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

105×	`p16-lft-identity-expand` `p16--un-lft-identity`
84×	`p16-times-frac`
76×	`*p16-rgt-identity-expand`
43×	`associate-r`
36×	`introduce-quire`
31×	`associate-l`
26×	`insert-quire-fdp-add`
20×	`p16-distribute-lft-out` `distribute-lft-out`
17×	`/p16-rgt-identity-expand`
16×	`distribute-lft-out--`
13×	`associate-/r/`
12×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
10×	`distribute-rgt-out` `-p16-rgt-identity-expand`
8×	`distribute-rgt-out--`
4×	`associate-+l+` `associate-+r+`
3×	`insert-quire-fdp-sub`
2×	`distribute-rgt-in` `+-commutative` `associate-+r-` `insert-quire-add` `distribute-lft-in` `associate--l+` `associate-+l-` `associate--r+`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `associate-l/` `associate-r/` `p16-flip--` `*-commutative` `associate--r-`

Counts

4 → 193

Calls

4 calls:

23.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
23.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
23.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
21.0ms	(*.p16 (/.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
0.0ms	(*.p16 (/.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))))

simplify2.2s

Counts

197 → 197

Iterations

Iter	Nodes
done	2008
3	2008
2	450
1	108
0	50

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.4b

regimes137.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	7

end0.0ms

sample1.9s

Algorithm: halfpoints