Details

sample62.0ms

Algorithm: halfpoints

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize111.0ms

Local error

Found 2 expressions with local error:

0.2b	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.7b	(-.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)))
9.0ms	(-.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))

simplify4.9s

Counts

53 → 53

Iterations

Iter	Nodes
done	5001
3	3672
2	295
1	52
0	29

prune292.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize280.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
0.3b	(*.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.5b	(-.p16 (.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) x)))
0.8b	(/.p16 (-.p16 (.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) x))) (+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

86×	`p16-lft-identity-expand` `p16--un-lft-identity`
70×	`p16-times-frac`
56×	`*p16-rgt-identity-expand`
24×	`p16-distribute-lft-out` `distribute-lft-out`
15×	`difference-of-squares`
14×	`+p16-lft-identity-expand` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand`
13×	`associate-/r` `associate-r` `associate-l*`
12×	`distribute-rgt-out`
10×	`introduce-quire`
9×	`associate-/r/`
8×	`-p16-rgt-identity-expand`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `associate--r+`
4×	`associate-/l*`
3×	`insert-quire-fdp-add`
2×	`associate-+l+` `associate-+r+` `p16-flip--` `associate-/l/`
1×	`associate--l-` `+-commutative` `insert-quire-sub` `associate-+r-` `sub-neg` `insert-quire-add` `associate-l/` `associate-r/` `*-commutative` `associate-+l-` `insert-quire-fdp-sub` `associate--r-`

Counts

4 → 177

Calls

4 calls:

13.0ms	(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
4.0ms	(*.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
3.0ms	(-.p16 (.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) x)))
52.0ms	(/.p16 (-.p16 (.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) x))) (+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.6s

Counts

181 → 181

Iterations

Iter	Nodes
done	5001
2	2115
1	166
0	67

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.4b

localize321.0ms

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))))
0.7b	(-.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)) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

80×	`p16-lft-identity-expand` `p16--un-lft-identity`
57×	`p16-times-frac`
54×	`*p16-rgt-identity-expand`
43×	`associate-r`
36×	`introduce-quire`
26×	`insert-quire-fdp-add`
20×	`p16-distribute-lft-out` `distribute-lft-out`
16×	`/p16-rgt-identity-expand`
12×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
10×	`distribute-rgt-out` `-p16-rgt-identity-expand`
9×	`associate-/r/`
6×	`associate-*l/`
4×	`associate-+l+` `associate-+r+` `distribute-lft-out--`
3×	`insert-quire-fdp-sub`
2×	`distribute-rgt-in` `+-commutative` `associate-+r-` `insert-quire-add` `distribute-lft-in` `distribute-rgt-out--` `associate--l+` `associate-*r/` `p16-flip--` `associate-+l-` `associate--r+`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `associate-l` `*-commutative` `associate--r-`

Counts

4 → 166

Calls

4 calls:

22.0ms	(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
24.0ms	(+.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))
39.0ms	(.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 (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)) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))))

simplify1.7s

Counts

170 → 170

Iterations

Iter	Nodes
done	5000
2	1097
1	121
0	50

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize157.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.3b	(/.p16 (real->posit16 1.0) (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))
0.3b	(/.p16 (real->posit16 1.0) (/.p16 (real->posit16 1.0) (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))))
0.7b	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

240×	`p16-times-frac`
180×	`p16-lft-identity-expand` `p16--un-lft-identity`
163×	`*p16-rgt-identity-expand`
68×	`distribute-lft-out--`
44×	`associate-/r*`
34×	`distribute-rgt-out--`
30×	`/p16-rgt-identity-expand`
29×	`associate-/r/`
9×	`associate-/l*`
8×	`introduce-quire`
6×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `p16-flip--` `+p16-rgt-identity-expand`
3×	`insert-quire-fdp-sub` `associate-/l/`
2×	`associate--l+` `associate--r+`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `remove-double-div.p16` `associate--r-`

Counts

4 → 243

Calls

4 calls:

3.0ms	(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
16.0ms	(/.p16 (real->posit16 1.0) (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))
24.0ms	(/.p16 (real->posit16 1.0) (/.p16 (real->posit16 1.0) (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))))
9.0ms	(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.2s

Counts

247 → 247

Iterations

Iter	Nodes
done	5000
2	556
1	76
0	41

prune650.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.4b

regimes171.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	9
1	9
0	7

end0.0ms

sample1.8s

Algorithm: halfpoints