Details

sample64.0ms

Algorithm: halfpoints

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
2	15
1	14
0	9

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize160.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.p16 (+.p16 x (real->posit16 1)))
0.2b	(/.p16 (real->posit16 1) (sqrt.p16 x))
0.2b	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.4b	(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

rewrite43.0ms

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))
2.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
34.0ms	(-.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

Iter	Nodes
done	5027
3	1366
2	269
1	68
0	42

prune809.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize293.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

109×	`p16-lft-identity-expand` `p16--un-lft-identity`
104×	`p16-times-frac`
85×	`*p16-rgt-identity-expand`
82×	`associate-l`
48×	`associate-r`
36×	`introduce-quire` `distribute-lft-out--`
31×	`insert-quire-fdp-sub`
22×	`/p16-rgt-identity-expand`
14×	`distribute-rgt-out--`
12×	`associate-/r` `+p16-lft-identity-expand` `associate-/r/` `+p16-rgt-identity-expand` `associate-/l`
9×	`associate-l/` `associate-r/`
6×	`distribute-rgt-in` `distribute-lft-in` `-p16-rgt-identity-expand` `associate--l+` `*-commutative` `associate--r+`
4×	`difference-of-squares` `associate-/l/`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `p16-flip--` `associate--r-`

Counts

4 → 217

Calls

4 calls:

4.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
4.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
11.0ms	(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
91.0ms	(-.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 (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))))))

simplify2.7s

Counts

221 → 221

Iterations

Iter	Nodes
done	5032
3	2543
2	532
1	167
0	71

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize327.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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:

3.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
30.0ms	(-.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	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
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

142 → 142

Iterations

Iter	Nodes
done	5019
3	1329
2	239
1	63
0	38

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize333.0ms

Local error

Found 4 expressions with local error:

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

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

297×	`p16-times-frac`
210×	`p16-lft-identity-expand` `p16--un-lft-identity`
163×	`*p16-rgt-identity-expand`
102×	`associate-r`
85×	`associate-l`
72×	`introduce-quire`
67×	`insert-quire-fdp-sub`
48×	`distribute-lft-out--`
30×	`associate-/l*`
27×	`/p16-rgt-identity-expand`
17×	`associate-/r/`
14×	`associate-/l/`
12×	`associate-/r*`
11×	`distribute-rgt-out--`
9×	`associate-r/` `-commutative`
8×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`-p16-rgt-identity-expand` `associate--l+`
2×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `associate-*l/` `p16-flip--` `associate--r-`

Counts

4 → 304

Calls

4 calls:

13.0ms	(/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms	(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
184.0ms	(-.p16 (.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (/.p16 (.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.8s

Counts

308 → 308

Iterations

Iter	Nodes
done	5003
3	3322
2	998
1	206
0	100

prune1.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

regimes100.0ms

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	11
1	11
0	9

end0.0ms

sample2.2s

Algorithm: halfpoints