Details

sample90.0ms

Algorithm: halfpoints

simplify1.3s

Counts

1 → 1

Iterations

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

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize241.0ms

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.im)
0.2b	(+.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))

rewrite28.0ms

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-+r+` `associate-l`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `associate-*l/` `associate--l+` `p16-flip--` `insert-quire-fdp-add` `associate-+l-` `associate--r+` `difference-of-squares`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `*-commutative` `insert-quire-fdp-sub` `associate--r-`

Counts

4 → 68

Calls

4 calls:

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

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	2028
4	2028
3	1021
2	224
1	84
0	46

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize267.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (+.p16 x.im x.im) x.re)
0.1b	(*.p16 (+.p16 x.im x.re) x.im)
0.2b	(.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.im))
9.5b	(quire16-mul-add (posit16->quire16 (.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.im))) (*.p16 (+.p16 x.im x.im) x.re) x.re)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

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

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify872.0ms

Counts

51 → 51

Iterations

Iter	Nodes
done	2016
4	2016
3	688
2	167
1	61
0	28

prune2.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize420.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (+.p16 x.im x.re) x.im)
0.2b	(.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.im))
0.3b	(.p16 (.p16 x.re x.re) (+.p16 x.im x.im))
9.6b	(quire16-mul-add (posit16->quire16 (.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.im))) (.p16 (.p16 x.re x.re) (+.p16 x.im x.im)) (real->posit16 1.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

6.0ms	(*.p16 (+.p16 x.im x.re) x.im)
12.0ms	(.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.im))
10.0ms	(.p16 (.p16 x.re x.re) (+.p16 x.im x.im))
1.0ms	(quire16-mul-add (posit16->quire16 (.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.im))) (.p16 (.p16 x.re x.re) (+.p16 x.im x.im)) (real->posit16 1.0))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.p16 (+.p16 x.im x.re) x.im)
0.0ms	(.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.im))
0.0ms	(.p16 (.p16 x.re x.re) (+.p16 x.im x.im))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.im))) (.p16 (.p16 x.re x.re) (+.p16 x.im x.im)) (real->posit16 1.0))

simplify1.5s

Counts

55 → 55

Iterations

Iter	Nodes
done	2108
4	2108
3	1544
2	253
1	77
0	31

prune2.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize343.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (.p16 x.re x.im) (.p16 x.im x.re))
0.2b	(.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.re x.re)) x.im x.im)) x.im)
0.2b	(+.p16 (.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.re x.re)) x.im x.im)) x.im) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re))
6.2b	(quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

5.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.im x.re))
4.0ms	(.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.re x.re)) x.im x.im)) x.im)
7.0ms	(+.p16 (.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.re x.re)) x.im x.im)) x.im) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re))
0.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im 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 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.re x.re)) x.im x.im)) x.im)
0.0ms	(+.p16 (.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.re x.re)) x.im x.im)) x.im) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re))
0.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)

simplify1.4s

Counts

51 → 51

Iterations

Iter	Nodes
done	2044
5	2044
4	855
3	232
2	84
1	44
0	31

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes344.0ms

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

sample3.2s

Algorithm: halfpoints