Details

sample91.0ms

Algorithm: halfpoints

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1196
4	300
3	113
2	53
1	21
0	11

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize188.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.p16 x.im (+.p16 x.im x.im))
0.1b	(*.p16 x.im (+.p16 x.im (+.p16 x.im x.im)))
0.2b	(.p16 x.re (-.p16 (.p16 x.re x.re) (*.p16 x.im (+.p16 x.im (+.p16 x.im x.im)))))
0.3b	(-.p16 (.p16 x.re x.re) (.p16 x.im (+.p16 x.im (+.p16 x.im x.im))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

7.0ms	(+.p16 x.im (+.p16 x.im x.im))
8.0ms	(*.p16 x.im (+.p16 x.im (+.p16 x.im x.im)))
8.0ms	(.p16 x.re (-.p16 (.p16 x.re x.re) (*.p16 x.im (+.p16 x.im (+.p16 x.im x.im)))))
7.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im (+.p16 x.im (+.p16 x.im x.im))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	452
1	88
0	43

prune741.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize246.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.p16 (+.p16 x.im x.im) x.im)
0.1b	(*.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))
0.2b	(.p16 x.re (-.p16 (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)) (*.p16 (+.p16 x.im x.im) x.im)))
0.3b	(-.p16 (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)) (.p16 (+.p16 x.im x.im) x.im))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

24×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
18×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
11×	`sub-neg`
8×	`p16-lft-identity-expand` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
6×	`introduce-quire` `associate-r` `associate-l`
4×	`associate-*r/`
3×	`p16-flip--` `*-commutative` `associate--r-`
2×	`associate-*l/` `associate--r+`
1×	`associate--l-` `insert-quire-sub` `insert-quire-fdp-sub`

Counts

4 → 99

Calls

4 calls:

6.0ms	(*.p16 (+.p16 x.im x.im) x.im)
9.0ms	(*.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))
9.0ms	(.p16 x.re (-.p16 (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)) (*.p16 (+.p16 x.im x.im) x.im)))
7.0ms	(-.p16 (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)) (.p16 (+.p16 x.im x.im) x.im))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.8s

Counts

103 → 103

Iterations

Iter	Nodes
done	5002
2	1675
1	188
0	78

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize354.0ms

Local error

Found 3 expressions with local error:

0.1b

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

0.2b

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

6.3b

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`+p16-lft-identity-expand` `associate-r` `+p16-rgt-identity-expand`
5×	`distribute-rgt-in` `p16-lft-identity-expand` `distribute-lft-in` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
3×	`associate-l` `associate-*r/`
2×	`sub-neg` `introduce-quire` `-p16-rgt-identity-expand` `*-commutative`
1×	`associate-*l/` `p16-flip--`

Counts

3 → 41

Calls

3 calls:

9.0ms

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

4.0ms

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

1.0ms

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

series0.0ms

Counts

3 → 3

Calls

3 calls:

0.0ms

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

0.0ms

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

0.0ms

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

simplify881.0ms

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
2	520
1	76
0	33

prune673.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize303.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (.p16 x.re x.im) (.p16 x.im x.re))
0.2b	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.re)
0.3b	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))
0.4b	(-.p16 (.p16 (-.p16 (.p16 x.re x.re) (.p16 x.im x.im)) x.re) (.p16 (+.p16 (.p16 x.re x.im) (.p16 x.im x.re)) x.im))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
5×	`p16-lft-identity-expand` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
4×	`associate-l` `associate--l+` `associate--r+`
3×	`p16-flip--`
2×	`associate--l-` `insert-quire-sub` `associate-+l+` `associate-+r+` `sub-neg` `associate-*l/` `insert-quire-fdp-sub` `associate--r-` `difference-of-squares`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `*-commutative` `insert-quire-fdp-add` `associate-+l-`

Counts

4 → 69

Calls

4 calls:

6.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.im x.re))
5.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.re)
5.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))
5.0ms	(-.p16 (.p16 (-.p16 (.p16 x.re x.re) (.p16 x.im x.im)) x.re) (.p16 (+.p16 (.p16 x.re x.im) (.p16 x.im x.re)) x.im))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	4986
2	501
1	105
0	51

prune817.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes261.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
0	11

end0.0ms

sample2.9s

Algorithm: halfpoints