Details

sample122.0ms

Algorithm: halfpoints

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
7	4047
6	1485
5	622
4	223
3	106
2	51
1	21
0	11

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize239.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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

Counts

4 → 65

Calls

4 calls:

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

simplify696.0ms

Counts

69 → 69

Iterations

Iter	Nodes
3	2142
2	346
1	92
0	46

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize250.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (+.p16 x.re x.re) x.im)
0.1b	(*.p16 x.re (-.p16 x.re x.im))
0.2b	(.p16 (.p16 x.re (-.p16 x.re x.im)) (+.p16 x.im x.re))
8.3b	(quire16-mul-sub (posit16->quire16 (.p16 (.p16 x.re (-.p16 x.re x.im)) (+.p16 x.im x.re))) (*.p16 (+.p16 x.re x.re) x.im) x.im)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

6.0ms	(*.p16 (+.p16 x.re x.re) x.im)
4.0ms	(*.p16 x.re (-.p16 x.re x.im))
5.0ms	(.p16 (.p16 x.re (-.p16 x.re x.im)) (+.p16 x.im x.re))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 (.p16 x.re (-.p16 x.re x.im)) (+.p16 x.im x.re))) (*.p16 (+.p16 x.re x.re) x.im) x.im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.1s

Counts

56 → 56

Iterations

Iter	Nodes
4	6530
3	983
2	246
1	74
0	36

prune2.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize286.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.1b	(*.p16 (+.p16 x.re x.re) x.im)
0.2b	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
8.3b	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 (+.p16 x.re x.re) x.im) x.im)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

7.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
6.0ms	(*.p16 (+.p16 x.re x.re) x.im)
8.0ms	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 (+.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 (+.p16 x.re x.re) x.im)
0.0ms	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 (+.p16 x.re x.re) x.im) x.im)

simplify6.2s

Counts

59 → 59

Iterations

Iter	Nodes
4	12278
3	1306
2	296
1	77
0	38

prune2.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

localize316.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (-.p16 x.re x.im) x.re)
0.2b	(.p16 x.re (+.p16 (.p16 (-.p16 x.re x.im) x.im) (*.p16 (-.p16 x.re x.im) x.re)))
0.3b	(+.p16 (.p16 (-.p16 x.re x.im) x.im) (.p16 (-.p16 x.re x.im) x.re))
8.3b	(quire16-mul-sub (posit16->quire16 (.p16 x.re (+.p16 (.p16 (-.p16 x.re x.im) x.im) (.p16 (-.p16 x.re x.im) x.re)))) (.p16 (+.p16 x.re x.re) x.im) x.im)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

3.0ms	(*.p16 (-.p16 x.re x.im) x.re)
2.0ms	(.p16 x.re (+.p16 (.p16 (-.p16 x.re x.im) x.im) (*.p16 (-.p16 x.re x.im) x.re)))
4.0ms	(+.p16 (.p16 (-.p16 x.re x.im) x.im) (.p16 (-.p16 x.re x.im) x.re))
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (+.p16 (.p16 (-.p16 x.re x.im) x.im) (.p16 (-.p16 x.re x.im) x.re)))) (.p16 (+.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) x.re)
0.0ms	(.p16 x.re (+.p16 (.p16 (-.p16 x.re x.im) x.im) (*.p16 (-.p16 x.re x.im) x.re)))
0.0ms	(+.p16 (.p16 (-.p16 x.re x.im) x.im) (.p16 (-.p16 x.re x.im) x.re))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (+.p16 (.p16 (-.p16 x.re x.im) x.im) (.p16 (-.p16 x.re x.im) x.re)))) (.p16 (+.p16 x.re x.re) x.im) x.im)

simplify1.4s

Counts

54 → 54

Iterations

Iter	Nodes
5	2210
4	806
3	274
2	125
1	58
0	32

prune2.1s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0.0b

regimes292.0ms

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
1	11
0	11

end0.0ms

sample3.2s

Algorithm: halfpoints