Details

sample92.0ms

Algorithm: halfpoints

simplify5.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	4047
6	1485
5	622
4	223
3	106
2	51
1	21
0	11

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize351.0ms

Local error

Found 4 expressions with local error:

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

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

241×	`associate-l`
201×	`p16-lft-identity-expand` `p16--un-lft-identity`
180×	`distribute-lft-out--`
63×	`*p16-rgt-identity-expand`
49×	`p16-distribute-lft-out` `distribute-lft-out`
34×	`introduce-quire`
30×	`*-commutative`
28×	`insert-quire-fdp-sub`
16×	`distribute-rgt-out` `distribute-rgt-out--`
8×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand` `difference-of-squares`
6×	`/p16-rgt-identity-expand`
4×	`associate--l+` `associate--r+`
3×	`associate-*l/` `p16-flip--`
2×	`associate--l-` `insert-quire-sub` `sub-neg` `associate--r-`

Counts

4 → 243

Calls

4 calls:

9.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.im)
8.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.re)
119.0ms	(-.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))
17.0ms	(-.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.im)
0.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.re)
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))
0.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))

simplify2.0s

Counts

247 → 247

Iterations

Iter	Nodes
done	5010
3	2523
2	447
1	117
0	57

prune881.0ms

Pruning

7 alts after pruning (6 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.im) (+.p16 x.im x.re))
0.2b	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
0.3b	(.p16 (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) x.re)
9.1b	(quire16-mul-sub (posit16->quire16 (.p16 (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) x.re)) x.im (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

23×	`p16-lft-identity-expand` `p16--un-lft-identity`
17×	`associate-l`
15×	`*p16-rgt-identity-expand`
10×	`*-commutative`
9×	`introduce-quire`
8×	`associate-*l/` `/p16-rgt-identity-expand`
7×	`p16-distribute-lft-out` `+p16-lft-identity-expand` `distribute-rgt-out` `+p16-rgt-identity-expand` `distribute-lft-out`
6×	`associate-r`
5×	`-p16-rgt-identity-expand` `insert-quire-fdp-add`
4×	`distribute-rgt-in` `distribute-lft-in`
3×	`+-commutative`
2×	`associate-+l+` `associate-+r+` `distribute-lft1-in` `distribute-rgt1-in` `associate-*r/` `p16-flip--`
1×	`associate-+r-` `insert-quire-add` `associate-+l-`

Counts

4 → 96

Calls

4 calls:

18.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
21.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
15.0ms	(.p16 (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) x.re)
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) x.re)) x.im (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)))

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

simplify1.4s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	1628
2	255
1	87
0	45

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize262.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
0.2b	(*.p16 (+.p16 x.im x.re) x.re)
0.2b	(.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.re))
9.1b	(quire16-mul-sub (posit16->quire16 (.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.re))) x.im (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

22×	`p16-lft-identity-expand` `p16--un-lft-identity`
14×	`*p16-rgt-identity-expand`
10×	`*-commutative`
9×	`introduce-quire` `associate-l`
8×	`associate-r`
7×	`p16-distribute-lft-out` `+p16-lft-identity-expand` `distribute-rgt-out` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand` `distribute-lft-out`
5×	`-p16-rgt-identity-expand` `insert-quire-fdp-add`
4×	`associate-*l/`
2×	`distribute-rgt-in` `associate-+l+` `associate-+r+` `distribute-lft-in` `distribute-lft1-in` `distribute-rgt1-in` `associate-*r/`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `p16-flip--` `associate-+l-`

Counts

4 → 87

Calls

4 calls:

19.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
3.0ms	(*.p16 (+.p16 x.im x.re) x.re)
8.0ms	(.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.re))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.re))) x.im (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.3s

Counts

91 → 91

Iterations

Iter	Nodes
done	5036
3	1334
2	255
1	75
0	38

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize398.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.p16 x.re (+.p16 x.im x.im))
0.2b	(*.p16 (+.p16 x.im x.re) x.re)
0.2b	(.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.re))
9.1b	(quire16-mul-sub (posit16->quire16 (.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.re))) x.im (*.p16 x.re (+.p16 x.im x.im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

8.0ms	(*.p16 x.re (+.p16 x.im x.im))
7.0ms	(*.p16 (+.p16 x.im x.re) x.re)
15.0ms	(.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.re))
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.re))) x.im (*.p16 x.re (+.p16 x.im x.im)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.3s

Counts

66 → 66

Iterations

Iter	Nodes
done	5031
3	1236
2	196
1	66
0	33

prune646.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes307.0ms

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