Details

sample104.0ms

Algorithm: halfpoints

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	16
0	11

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize219.0ms

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))
1.0b	(/.p16 (-.p16 (.p16 x.im y.re) (.p16 x.re y.im)) (+.p16 (.p16 y.re y.re) (.p16 y.im y.im)))

rewrite12.0ms

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:

4.0ms	(+.p16 (.p16 y.re y.re) (.p16 y.im y.im))
2.0ms	(-.p16 (.p16 x.im y.re) (.p16 x.re y.im))
4.0ms	(/.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)))

simplify2.2s

Counts

64 → 64

Iterations

Iter	Nodes
done	5020
3	2194
2	345
1	76
0	42

prune571.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize237.0ms

Local error

Found 3 expressions with local error:

0.2b

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

1.0b

(/.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)))

6.3b

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

rewrite16.0ms

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))

7.0ms

(/.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)))

1.0ms

(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)

simplify4.8s

Counts

45 → 45

Iterations

Iter	Nodes
done	5000
4	1082
3	239
2	86
1	37
0	30

prune695.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize288.0ms

Local error

Found 3 expressions with local error:

1.0b

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

5.4b

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

6.3b

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

9×	`p16-lft-identity-expand` `p16-times-frac` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
3×	`associate-/r` `/p16-rgt-identity-expand` `associate-/l`
1×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `associate-/r/` `+p16-rgt-identity-expand` `associate-/l/`

Counts

3 → 25

Calls

3 calls:

2.0ms

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

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

0.0ms

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

simplify122.0ms

Counts

28 → 28

Iterations

Iter	Nodes
done	102
7	102
6	101
5	94
4	85
3	75
2	58
1	26
0	24

prune403.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.8b

localize303.0ms

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)) (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.im y.re)) x.re y.im))))
1.1b	(/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.im y.re)) x.re y.im)))
5.4b	(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)
6.3b	(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

84×	`p16-times-frac`
52×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
16×	`associate-/r*`
9×	`/p16-rgt-identity-expand`
6×	`associate-/r/` `associate-/l*`
2×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand` `associate-/l/`

Counts

4 → 90

Calls

4 calls:

16.0ms	(/.p16 (real->posit16 1.0) (/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.im y.re)) x.re y.im))))
3.0ms	(/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.im y.re)) x.re y.im)))
0.0ms	(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)
1.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re 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)) (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.im y.re)) x.re y.im))))
0.0ms	(/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.im y.re)) x.re y.im)))
0.0ms	(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)
0.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

simplify1.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	1053
6	1053
5	1045
4	997
3	587
2	99
1	45
0	32

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.7b

regimes1.3s

Accuracy

0% (0.4b remaining)

Error of 1.0b against oracle of 0.6b and baseline of 1.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
0	13

end0.0ms

sample3.9s

Algorithm: halfpoints