Details

sample124.0ms

Algorithm: halfpoints

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
7	2002
6	1308
5	586
4	220
3	107
2	49
1	20
0	11

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize238.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

2.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
3.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
4.0ms	(+.p16 (.p16 (-.p16 (.p16 x.re x.re) (.p16 x.im x.im)) x.im) (.p16 (+.p16 (.p16 x.re x.im) (.p16 x.im x.re)) x.re))
4.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.3s

Counts

68 → 68

Iterations

Iter	Nodes
done	2087
4	2087
3	1030
2	244
1	79
0	41

prune2.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize381.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 x.im (-.p16 x.re x.im))
0.1b	(.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))
0.2b	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
7.3b	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))) (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)) x.re)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

4.0ms	(*.p16 x.im (-.p16 x.re x.im))
9.0ms	(.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))
7.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
1.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))) (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)) x.re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.p16 x.im (-.p16 x.re x.im))
0.0ms	(.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))
0.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))) (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)) x.re)

simplify1.2s

Counts

63 → 63

Iterations

Iter	Nodes
done	2033
4	2033
3	1230
2	264
1	92
0	44

prune2.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize229.0ms

Local error

Found 4 expressions with local error:

0.1b	(.p16 (+.p16 (.p16 x.im x.re) (*.p16 x.im (neg.p16 x.im))) (+.p16 x.im x.re))
0.2b	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
0.3b	(+.p16 (.p16 x.im x.re) (.p16 x.im (neg.p16 x.im)))
7.3b	(quire16-mul-add (posit16->quire16 (.p16 (+.p16 (.p16 x.im x.re) (.p16 x.im (neg.p16 x.im))) (+.p16 x.im x.re))) (+.p16 (.p16 x.im x.re) (*.p16 x.im x.re)) x.re)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
8×	`associate-+r+`
7×	`introduce-quire` `-p16-rgt-identity-expand`
5×	`p16-lft-identity-expand` `associate-l` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
4×	`associate-+l+`
3×	`distribute-rgt-in` `p16-distribute-lft-out` `distribute-lft-in` `associate-r` `distribute-lft-out`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `insert-quire-fdp-add` `associate-+l-`
1×	`distribute-rgt-out` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 64

Calls

4 calls:

3.0ms	(.p16 (+.p16 (.p16 x.im x.re) (*.p16 x.im (neg.p16 x.im))) (+.p16 x.im x.re))
4.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
4.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im (neg.p16 x.im)))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (+.p16 (.p16 x.im x.re) (.p16 x.im (neg.p16 x.im))) (+.p16 x.im x.re))) (+.p16 (.p16 x.im x.re) (*.p16 x.im x.re)) x.re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(.p16 (+.p16 (.p16 x.im x.re) (*.p16 x.im (neg.p16 x.im))) (+.p16 x.im x.re))
0.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
0.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im (neg.p16 x.im)))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (+.p16 (.p16 x.im x.re) (.p16 x.im (neg.p16 x.im))) (+.p16 x.im x.re))) (+.p16 (.p16 x.im x.re) (*.p16 x.im x.re)) x.re)

simplify1.0s

Counts

68 → 68

Iterations

Iter	Nodes
done	2088
4	2088
3	1034
2	287
1	93
0	42

prune3.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize329.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 x.im (+.p16 x.im x.re))
0.2b	(.p16 (-.p16 x.re x.im) (.p16 x.im (+.p16 x.im x.re)))
0.2b	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
7.3b	(quire16-mul-add (posit16->quire16 (quire16->posit16 (posit16->quire16 (.p16 (-.p16 x.re x.im) (.p16 x.im (+.p16 x.im x.re)))))) (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)) x.re)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`distribute-rgt-in` `distribute-lft-in` `+p16-lft-identity-expand` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand`
5×	`p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
4×	`associate-r` `associate-*r/`
3×	`associate-l`
2×	`associate-+l+` `associate-+r+` `associate-l/` `-commutative`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `p16-distribute-lft-out` `distribute-rgt-out` `p16-flip--` `insert-quire-fdp-add` `associate-+l-` `distribute-lft-out`

Counts

4 → 60

Calls

4 calls:

3.0ms	(*.p16 x.im (+.p16 x.im x.re))
5.0ms	(.p16 (-.p16 x.re x.im) (.p16 x.im (+.p16 x.im x.re)))
4.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
0.0ms	(quire16-mul-add (posit16->quire16 (quire16->posit16 (posit16->quire16 (.p16 (-.p16 x.re x.im) (.p16 x.im (+.p16 x.im x.re)))))) (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)) x.re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.p16 x.im (+.p16 x.im x.re))
0.0ms	(.p16 (-.p16 x.re x.im) (.p16 x.im (+.p16 x.im x.re)))
0.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
0.0ms	(quire16-mul-add (posit16->quire16 (quire16->posit16 (posit16->quire16 (.p16 (-.p16 x.re x.im) (.p16 x.im (+.p16 x.im x.re)))))) (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)) x.re)

simplify1.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	2006
3	2006
2	365
1	90
0	44

prune2.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes239.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
0	11

end0.0ms

sample2.9s

Algorithm: halfpoints