Details

sample80.0ms

Algorithm: halfpoints

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2018
7	2018
6	1485
5	622
4	223
3	106
2	51
1	21
0	11

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize196.0ms

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))))

rewrite38.0ms

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:

9.0ms	(+.p16 x.im (+.p16 x.im x.im))
10.0ms	(*.p16 x.im (+.p16 x.im (+.p16 x.im x.im)))
10.0ms	(.p16 x.re (-.p16 (.p16 x.re x.re) (*.p16 x.im (+.p16 x.im (+.p16 x.im x.im)))))
9.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im (+.p16 x.im (+.p16 x.im x.im))))

series8.0ms

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))))

simplify1.4s

Counts

76 → 76

Iterations

Iter	Nodes
done	2057
4	2057
3	1766
2	286
1	84
0	43

prune739.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize133.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

3.0ms	(*.p16 x.im (+.p16 x.im x.im))
13.0ms	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))
5.0ms	(.p16 x.re (-.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (*.p16 x.im (+.p16 x.im x.im))))
3.0ms	(-.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re 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 (+.p16 x.im x.re) (-.p16 x.re x.im))
0.0ms	(.p16 x.re (-.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (*.p16 x.im (+.p16 x.im x.im))))
0.0ms	(-.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (.p16 x.im (+.p16 x.im x.im)))

simplify1.5s

Counts

107 → 107

Iterations

Iter	Nodes
done	2000
3	2000
2	596
1	192
0	79

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize187.0ms

Local error

Found 3 expressions with local error:

0.1b

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

0.2b

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

6.6b

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

11.0ms

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

2.0ms

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

0.0ms

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

series0.0ms

Counts

3 → 3

Calls

3 calls:

0.0ms

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

0.0ms

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

0.0ms

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

simplify2.1s

Counts

44 → 44

Iterations

Iter	Nodes
done	2084
4	2084
3	1205
2	235
1	76
0	33

prune598.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize230.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.p16 (+.p16 x.im x.re) x.re)
0.2b	(.p16 x.re (quire16->posit16 (quire16-mul-sub (posit16->quire16 (+.p16 (.p16 (+.p16 x.im x.re) x.re) (*.p16 (+.p16 x.im x.re) (neg.p16 x.im)))) x.im (+.p16 x.im x.im))))
0.4b	(+.p16 (.p16 (+.p16 x.im x.re) x.re) (.p16 (+.p16 x.im x.re) (neg.p16 x.im)))
6.6b	(quire16-mul-sub (posit16->quire16 (+.p16 (.p16 (+.p16 x.im x.re) x.re) (.p16 (+.p16 x.im x.re) (neg.p16 x.im)))) x.im (+.p16 x.im x.im))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

4.0ms	(*.p16 (+.p16 x.im x.re) x.re)
2.0ms	(.p16 x.re (quire16->posit16 (quire16-mul-sub (posit16->quire16 (+.p16 (.p16 (+.p16 x.im x.re) x.re) (*.p16 (+.p16 x.im x.re) (neg.p16 x.im)))) x.im (+.p16 x.im x.im))))
4.0ms	(+.p16 (.p16 (+.p16 x.im x.re) x.re) (.p16 (+.p16 x.im x.re) (neg.p16 x.im)))
0.0ms	(quire16-mul-sub (posit16->quire16 (+.p16 (.p16 (+.p16 x.im x.re) x.re) (.p16 (+.p16 x.im x.re) (neg.p16 x.im)))) x.im (+.p16 x.im x.im))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.7s

Counts

57 → 57

Iterations

Iter	Nodes
done	2022
4	2022
3	817
2	154
1	68
0	35

prune764.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes265.0ms

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	10
0	10

end0.0ms

sample2.4s

Algorithm: halfpoints