Details

sample73.0ms

Algorithm: halfpoints

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	16
0	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize285.0ms

Local error

Found 3 expressions with local error:

0.2b	(+.p16 (.p16 y.re y.re) (.p16 y.im y.im))
0.3b	(-.p16 (.p16 x.im y.re) (.p16 x.re y.im))
0.9b	(/.p16 (-.p16 (.p16 x.im y.re) (.p16 x.re y.im)) (+.p16 (.p16 y.re y.re) (.p16 y.im y.im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
9×	`p16-times-frac`
7×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
5×	`/p16-rgt-identity-expand`
3×	`associate-/r` `associate-/l`
2×	`associate-+l+` `associate-+r+` `associate--l+` `p16-flip--` `associate--r+` `associate-/l/`
1×	`associate--l-` `+-commutative` `insert-quire-sub` `associate-+r-` `sub-neg` `insert-quire-add` `associate-/r/` `insert-quire-fdp-add` `associate-+l-` `insert-quire-fdp-sub` `associate--r-`

Counts

3 → 61

Calls

3 calls:

8.0ms	(+.p16 (.p16 y.re y.re) (.p16 y.im y.im))
5.0ms	(-.p16 (.p16 x.im y.re) (.p16 x.re y.im))
7.0ms	(/.p16 (-.p16 (.p16 x.im y.re) (.p16 x.re y.im)) (+.p16 (.p16 y.re y.re) (.p16 y.im y.im)))

series0.0ms

Counts

3 → 3

Calls

3 calls:

0.0ms	(+.p16 (.p16 y.re y.re) (.p16 y.im y.im))
0.0ms	(-.p16 (.p16 x.im y.re) (.p16 x.re y.im))
0.0ms	(/.p16 (-.p16 (.p16 x.im y.re) (.p16 x.re y.im)) (+.p16 (.p16 y.re y.re) (.p16 y.im y.im)))

simplify875.0ms

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	437
1	76
0	42

prune617.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.6b

localize292.0ms

Local error

Found 3 expressions with local error:

0.2b

(+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im))

0.9b

(/.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)) (+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im)))

6.7b

(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
9×	`p16-times-frac`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`associate-/r` `associate-/l`
2×	`associate-+l+` `associate-+r+`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `associate-/r/` `insert-quire-fdp-add` `associate-+l-` `associate-/l/`

Counts

3 → 42

Calls

3 calls:

8.0ms

(+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im))

16.0ms

(/.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)) (+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im)))

0.0ms

(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

series0.0ms

Counts

3 → 3

Calls

3 calls:

0.0ms

(+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im))

0.0ms

(/.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)) (+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im)))

0.0ms

(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

simplify7.1s

Counts

45 → 45

Iterations

Iter	Nodes
done	5001
3	1887
2	122
1	37
0	30

prune639.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.6b

localize301.0ms

Local error

Found 3 expressions with local error:

0.3b

(-.p16 (*.p16 x.im y.re) (*.p16 x.re y.im))

0.9b

(/.p16 (-.p16 (*.p16 x.im y.re) (*.p16 x.re y.im)) (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)))

3.9b

(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
9×	`p16-times-frac`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`associate-/r` `associate-/l`
2×	`associate--l+` `p16-flip--` `associate--r+` `associate-/l/`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `associate-/r/` `insert-quire-fdp-sub` `associate--r-`

Counts

3 → 44

Calls

3 calls:

4.0ms

(-.p16 (*.p16 x.im y.re) (*.p16 x.re y.im))

3.0ms

(/.p16 (-.p16 (*.p16 x.im y.re) (*.p16 x.re y.im)) (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)))

0.0ms

(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)

series0.0ms

Counts

3 → 3

Calls

3 calls:

0.0ms

(-.p16 (*.p16 x.im y.re) (*.p16 x.re y.im))

0.0ms

(/.p16 (-.p16 (*.p16 x.im y.re) (*.p16 x.re y.im)) (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)))

0.0ms

(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)

simplify8.3s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
3	4971
2	357
1	65
0	36

prune616.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize403.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (real->posit16 1.0) (/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (-.p16 (.p16 x.im y.re) (*.p16 x.re y.im))))
0.3b	(-.p16 (.p16 x.im y.re) (.p16 x.re y.im))
1.0b	(/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (-.p16 (.p16 x.im y.re) (*.p16 x.re y.im)))
3.9b	(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

87×	`p16-times-frac`
54×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
17×	`associate-/r*`
11×	`associate-/r/`
10×	`/p16-rgt-identity-expand`
6×	`p16-flip--` `associate-/l*`
5×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
2×	`associate--l+` `associate--r+` `associate-/l/`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `insert-quire-fdp-sub` `associate--r-`

Counts

4 → 113

Calls

4 calls:

5.0ms	(/.p16 (real->posit16 1.0) (/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (-.p16 (.p16 x.im y.re) (*.p16 x.re y.im))))
5.0ms	(-.p16 (.p16 x.im y.re) (.p16 x.re y.im))
3.0ms	(/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (-.p16 (.p16 x.im y.re) (*.p16 x.re y.im)))
0.0ms	(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1.0) (/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (-.p16 (.p16 x.im y.re) (*.p16 x.re y.im))))
0.0ms	(-.p16 (.p16 x.im y.re) (.p16 x.re y.im))
0.0ms	(/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (-.p16 (.p16 x.im y.re) (*.p16 x.re y.im)))
0.0ms	(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)

simplify1.6s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	562
1	83
0	46

prune1.1s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0.5b

regimes1.4s

Accuracy

0% (0.5b remaining)

Error of 1.1b against oracle of 0.6b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
0	12

end0.0ms

sample3.1s

Algorithm: halfpoints