Details

sample100.0ms

Algorithm: halfpoints

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4047
5	1267
4	334
3	115
2	51
1	20
0	11

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize220.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

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:

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

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	2715
2	351
1	87
0	46

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize219.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 x.re (+.p16 x.im x.im))
0.1b	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.2b	(.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
9.4b	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

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

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.5s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
3	4968
2	452
1	89
0	42

prune979.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize246.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 x.re (+.p16 x.im x.im))
0.2b	(.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))
0.2b	(*.p16 x.im (-.p16 x.re x.im))
9.4b	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

6.0ms	(*.p16 x.re (+.p16 x.im x.im))
9.0ms	(.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))
6.0ms	(*.p16 x.im (-.p16 x.re x.im))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.4s

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
3	3158
2	398
1	88
0	36

prune756.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize253.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (.p16 x.im (-.p16 x.re x.im)) x.im)
0.2b	(.p16 (.p16 x.im (-.p16 x.re x.im)) x.re)
0.5b	(+.p16 (.p16 (.p16 x.im (-.p16 x.re x.im)) x.im) (.p16 (.p16 x.im (-.p16 x.re x.im)) x.re))
9.4b	(quire16-mul-add (posit16->quire16 (+.p16 (.p16 (.p16 x.im (-.p16 x.re x.im)) x.im) (.p16 (.p16 x.im (-.p16 x.re x.im)) x.re))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 45

Calls

4 calls:

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

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify734.0ms

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
3	546
2	126
1	50
0	28

prune605.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes242.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
0	11

end0.0ms

sample2.8s

Algorithm: halfpoints