Details

sample582.0ms

Algorithm: halfpoints

simplify517.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2074
3	418
2	93
1	35
0	19

prune111.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize403.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0)))
0.2b	(+.p16 (.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0))))) (real->posit16 1.0))
0.5b	(/.p16 (+.p16 beta alpha) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0))))
0.6b	(.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

21×	`associate-r`
20×	`p16-lft-identity-expand` `p16--un-lft-identity`
14×	`/p16-rgt-identity-expand` `*p16-rgt-identity-expand`
10×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
8×	`introduce-quire`
6×	`associate-+l+` `p16-times-frac` `associate-l` `-p16-rgt-identity-expand` `associate-/r/`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`
4×	`p16-distribute-lft-out` `associate-*r/` `distribute-lft-out`
3×	`insert-quire-fdp-add` `associate-/l*`
2×	`associate-+r+` `*-commutative`
1×	`+-commutative` `associate-+r-` `associate-/r*` `insert-quire-add` `distribute-rgt-out` `p16-flip--` `associate-+l-` `associate-/l/`

Counts

4 → 98

Calls

4 calls:

45.0ms	(.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0)))
4.0ms	(+.p16 (.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0))))) (real->posit16 1.0))
6.0ms	(/.p16 (+.p16 beta alpha) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0))))
5.0ms	(.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0)))
0.0ms	(+.p16 (.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0))))) (real->posit16 1.0))
0.0ms	(/.p16 (+.p16 beta alpha) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0))))
0.0ms	(.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0)))))

simplify5.5s

Counts

102 → 102

Iterations

Iter	Nodes
3	7465
2	776
1	128
0	56

prune5.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize317.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0)))
0.3b	(.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha))))
0.5b	(.p16 (.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0))))
0.6b	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

109×	`p16-lft-identity-expand` `p16--un-lft-identity`
90×	`p16-times-frac`
67×	`*p16-rgt-identity-expand`
53×	`associate-r`
28×	`p16-distribute-lft-out` `distribute-lft-out`
15×	`associate-/r*`
13×	`/p16-rgt-identity-expand`
8×	`+p16-lft-identity-expand` `associate-*l/` `+p16-rgt-identity-expand`
7×	`distribute-rgt-out`
6×	`associate-/l*`
4×	`distribute-rgt-in` `distribute-lft-in` `introduce-quire` `associate-l` `-p16-rgt-identity-expand` `associate-/r/`
3×	`associate-*r/`
2×	`p16-flip--` `*-commutative` `associate-/l/`

Counts

4 → 177

Calls

4 calls:

88.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0)))
18.0ms	(.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha))))
37.0ms	(.p16 (.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0))))
14.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0)))
0.0ms	(.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha))))
0.0ms	(.p16 (.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0))))
0.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

simplify2.7s

Counts

181 → 181

Iterations

Iter	Nodes
3	5354
2	694
1	132
0	53

prune7.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize314.0ms

Local error

Found 4 expressions with local error:

0.3b	(.p16 (-.p16 beta alpha) (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 beta alpha))))
0.3b	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 beta alpha)))
0.5b	(.p16 (.p16 (-.p16 beta alpha) (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 beta alpha)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0))))
0.5b	(/.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 beta alpha))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

186×	`p16-times-frac`
130×	`p16-lft-identity-expand` `p16--un-lft-identity`
112×	`*p16-rgt-identity-expand`
83×	`associate-r`
18×	`/p16-rgt-identity-expand`
16×	`associate-/r*`
12×	`p16-distribute-lft-out` `distribute-lft-out`
11×	`associate-/r/`
8×	`+p16-lft-identity-expand` `associate-*l/` `+p16-rgt-identity-expand`
6×	`associate-/l*`
4×	`distribute-rgt-in` `distribute-lft-in` `introduce-quire` `associate-l` `-p16-rgt-identity-expand`
3×	`distribute-rgt-out` `associate-*r/`
2×	`p16-flip--` `*-commutative` `associate-/l/`

Counts

4 → 211

Calls

4 calls:

10.0ms	(.p16 (-.p16 beta alpha) (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 beta alpha))))
17.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 beta alpha)))
29.0ms	(.p16 (.p16 (-.p16 beta alpha) (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 beta alpha)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0))))
13.0ms	(/.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 beta alpha))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(.p16 (-.p16 beta alpha) (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 beta alpha))))
0.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 beta alpha)))
0.0ms	(.p16 (.p16 (-.p16 beta alpha) (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 beta alpha)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (real->posit16 2.0))))
0.0ms	(/.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 beta alpha))

simplify1.5s

Counts

215 → 215

Iterations

Iter	Nodes
3	2256
2	412
1	145
0	59

prune10.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.4b

localize522.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.p16 (real->posit16 1.0) (+.p16 beta (+.p16 (*.p16 i (real->posit16 2)) (+.p16 alpha (real->posit16 2.0)))))
0.3b	(.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha))))
0.5b	(.p16 (.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)))) (/.p16 (real->posit16 1.0) (+.p16 beta (+.p16 (.p16 i (real->posit16 2)) (+.p16 alpha (real->posit16 2.0))))))
0.6b	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

36×	`p16-times-frac`
35×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
26×	`associate-r`
13×	`/p16-rgt-identity-expand`
8×	`+p16-lft-identity-expand` `associate-*l/` `+p16-rgt-identity-expand`
6×	`associate-/r` `associate-/l`
4×	`distribute-rgt-in` `distribute-lft-in` `introduce-quire` `associate-l` `-p16-rgt-identity-expand` `associate-/r/`
3×	`associate-*r/`
2×	`p16-flip--` `*-commutative` `associate-/l/`

Counts

4 → 114

Calls

4 calls:

19.0ms	(/.p16 (real->posit16 1.0) (+.p16 beta (+.p16 (*.p16 i (real->posit16 2)) (+.p16 alpha (real->posit16 2.0)))))
17.0ms	(.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha))))
20.0ms	(.p16 (.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)))) (/.p16 (real->posit16 1.0) (+.p16 beta (+.p16 (.p16 i (real->posit16 2)) (+.p16 alpha (real->posit16 2.0))))))
25.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1.0) (+.p16 beta (+.p16 (*.p16 i (real->posit16 2)) (+.p16 alpha (real->posit16 2.0)))))
0.0ms	(.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha))))
0.0ms	(.p16 (.p16 (-.p16 beta alpha) (/.p16 (+.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)))) (/.p16 (real->posit16 1.0) (+.p16 beta (+.p16 (.p16 i (real->posit16 2)) (+.p16 alpha (real->posit16 2.0))))))
0.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

simplify1.8s

Counts

118 → 118

Iterations

Iter	Nodes
3	2507
2	672
1	138
0	58

prune5.7s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.4b

regimes1.4s

Accuracy

0% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 0.7b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
1	21
0	21

end0.0ms

sample14.3s

Algorithm: halfpoints