Details

sample106.0ms

Algorithm: halfpoints

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize77.0ms

Local error

Found 1 expressions with local error:

0.2b	(-.p16 (.p16 x.re y.re) (.p16 x.im y.im))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 18

Calls

1 calls:

2.0ms

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

series0.0ms

Counts

1 → 1

Calls

1 calls:

0.0ms

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

simplify505.0ms

Counts

19 → 19

Iterations

Iter	Nodes
done	2028
3	873
2	173
1	44
0	23

prune134.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize92.0ms

Local error

Found 1 expressions with local error:

5.2b	(quire16-mul-sub (posit16->quire16 (*.p16 x.re y.re)) x.im y.im)

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

1 → 0

Calls

1 calls:

0.0ms

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

series0.0ms

Counts

1 → 1

Calls

1 calls:

0.0ms

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

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	7

prune6.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize179.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.p16 (.p16 (.p16 x.re y.re) (.p16 x.re y.re)) (.p16 (.p16 x.im y.im) (.p16 x.im y.im)))
0.2b	(.p16 (.p16 x.re y.re) (*.p16 x.re y.re))
0.3b	(+.p16 (.p16 x.re y.re) (.p16 x.im y.im))
1.2b	(/.p16 (-.p16 (.p16 (.p16 x.re y.re) (.p16 x.re y.re)) (.p16 (.p16 x.im y.im) (.p16 x.im y.im))) (+.p16 (.p16 x.re y.re) (.p16 x.im y.im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

12.0ms	(-.p16 (.p16 (.p16 x.re y.re) (.p16 x.re y.re)) (.p16 (.p16 x.im y.im) (.p16 x.im y.im)))
9.0ms	(.p16 (.p16 x.re y.re) (*.p16 x.re y.re))
6.0ms	(+.p16 (.p16 x.re y.re) (.p16 x.im y.im))
20.0ms	(/.p16 (-.p16 (.p16 (.p16 x.re y.re) (.p16 x.re y.re)) (.p16 (.p16 x.im y.im) (.p16 x.im y.im))) (+.p16 (.p16 x.re y.re) (.p16 x.im y.im)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify476.0ms

Counts

95 → 95

Iterations

Iter	Nodes
done	2001
2	670
1	121
0	57

prune774.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize181.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (.p16 x.im y.im) (.p16 y.re x.re)) (.p16 (+.p16 (.p16 y.re x.re) (.p16 x.im y.im)) (-.p16 (.p16 y.re x.re) (*.p16 x.im y.im)))))
0.3b	(+.p16 (.p16 x.im y.im) (.p16 y.re x.re))
0.3b	(+.p16 (.p16 y.re x.re) (.p16 x.im y.im))
1.2b	(/.p16 (+.p16 (.p16 x.im y.im) (.p16 y.re x.re)) (.p16 (+.p16 (.p16 y.re x.re) (.p16 x.im y.im)) (-.p16 (.p16 y.re x.re) (*.p16 x.im y.im))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

45×	`p16-times-frac`
25×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
21×	`associate-/r/` `/p16-rgt-identity-expand`
11×	`associate-/r*`
10×	`associate-*r/`
8×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
6×	`associate-/l*`
5×	`associate-*l/` `p16-flip--`
4×	`associate-+l+` `associate-+r+`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `insert-quire-fdp-add` `associate-+l-` `associate-/l/`

Counts

4 → 107

Calls

4 calls:

3.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (.p16 x.im y.im) (.p16 y.re x.re)) (.p16 (+.p16 (.p16 y.re x.re) (.p16 x.im y.im)) (-.p16 (.p16 y.re x.re) (*.p16 x.im y.im)))))
3.0ms	(+.p16 (.p16 x.im y.im) (.p16 y.re x.re))
3.0ms	(+.p16 (.p16 y.re x.re) (.p16 x.im y.im))
3.0ms	(/.p16 (+.p16 (.p16 x.im y.im) (.p16 y.re x.re)) (.p16 (+.p16 (.p16 y.re x.re) (.p16 x.im y.im)) (-.p16 (.p16 y.re x.re) (*.p16 x.im y.im))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.0s

Counts

111 → 111

Iterations

Iter	Nodes
done	2029
3	1731
2	385
1	108
0	53

prune718.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes465.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	8
0	8

end0.0ms

sample2.2s

Algorithm: halfpoints