Details

sample105.0ms

Algorithm: halfpoints

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	11
0	7

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize99.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

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:

5.0ms

(-.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))

simplify8.5s

Counts

19 → 19

Iterations

Iter	Nodes
4	7916
3	873
2	173
1	44
0	23

prune495.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize110.0ms

Local error

Found 1 expressions with local error:

5.4b	(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)

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	8
1	8
0	7

prune25.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize223.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (.p16 x.im y.im) (*.p16 x.im y.im))
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)))
0.3b	(+.p16 (.p16 x.re y.re) (.p16 x.im y.im))
1.4b	(/.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)))

rewrite52.0ms

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 x.im y.im) (*.p16 x.im y.im))
15.0ms	(-.p16 (.p16 (.p16 x.re y.re) (.p16 x.re y.re)) (.p16 (.p16 x.im y.im) (.p16 x.im y.im)))
7.0ms	(+.p16 (.p16 x.re y.re) (.p16 x.im y.im))
15.0ms	(/.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 x.im y.im) (*.p16 x.im y.im))
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.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)))

simplify12.5s

Counts

95 → 95

Iterations

Iter	Nodes
3	3773
2	600
1	119
0	58

prune2.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize170.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

4.0ms	(+.p16 (.p16 x.re y.re) (.p16 x.im y.im))
3.0ms	(+.p16 (.p16 x.re y.re) (.p16 x.im y.im))
3.0ms	(/.p16 (+.p16 (.p16 x.re y.re) (.p16 x.im y.im)) (/.p16 (+.p16 (.p16 x.re y.re) (.p16 x.im y.im)) (-.p16 (.p16 x.re y.re) (.p16 x.im y.im))))
2.0ms	(/.p16 (+.p16 (.p16 x.re y.re) (.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 x.re y.re) (.p16 x.im y.im))
0.0ms	(+.p16 (.p16 x.re y.re) (.p16 x.im y.im))
0.0ms	(/.p16 (+.p16 (.p16 x.re y.re) (.p16 x.im y.im)) (/.p16 (+.p16 (.p16 x.re y.re) (.p16 x.im y.im)) (-.p16 (.p16 x.re y.re) (.p16 x.im y.im))))
0.0ms	(/.p16 (+.p16 (.p16 x.re y.re) (.p16 x.im y.im)) (-.p16 (.p16 x.re y.re) (.p16 x.im y.im)))

simplify4.8s

Counts

133 → 133

Iterations

Iter	Nodes
4	5983
3	1249
2	294
1	89
0	47

prune3.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes496.0ms

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
1	8
0	8

end0.0ms

sample3.1s

Algorithm: halfpoints