Details

sample63.0ms

Algorithm: halfpoints

simplify4.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
8	4615
7	3127
6	1308
5	586
4	220
3	107
2	49
1	20
0	11

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize189.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

434×	`associate-l`
369×	`p16-lft-identity-expand` `p16--un-lft-identity`
206×	`p16-distribute-lft-out` `distribute-lft-out`
112×	`distribute-lft-out--`
107×	`*p16-rgt-identity-expand`
36×	`*-commutative`
34×	`introduce-quire`
28×	`distribute-rgt-out--`
27×	`distribute-rgt-out`
23×	`insert-quire-fdp-add`
8×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand` `difference-of-squares`
6×	`/p16-rgt-identity-expand`
5×	`insert-quire-fdp-sub`
3×	`associate-*l/`
2×	`associate-+l+` `associate-+r+` `associate--l+` `p16-flip--` `associate--r+`
1×	`associate--l-` `+-commutative` `insert-quire-sub` `associate-+r-` `sub-neg` `insert-quire-add` `associate-+l-` `associate--r-`

Counts

4 → 362

Calls

4 calls:

9.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
8.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
113.0ms	(+.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))
9.0ms	(-.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.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))

simplify1.4s

Counts

366 → 366

Iterations

Iter	Nodes
done	5006
3	1320
2	310
1	96
0	52

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize356.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

22×	`p16-lft-identity-expand` `p16--un-lft-identity`
14×	`associate-l` `*p16-rgt-identity-expand`
10×	`*-commutative`
9×	`introduce-quire`
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/`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
2×	`associate-+l+` `associate-+r+` `sub-neg` `distribute-lft1-in` `distribute-rgt1-in` `associate-*r/`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `p16-flip--` `associate-+l-`

Counts

4 → 89

Calls

4 calls:

7.0ms	(*.p16 (+.p16 x.im x.re) x.im)
21.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
16.0ms	(.p16 (.p16 (+.p16 x.im x.re) x.im) (-.p16 x.re x.im))
1.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 (+.p16 x.im x.re) x.im) (-.p16 x.re x.im))) x.re (+.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) x.im)
0.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
0.0ms	(.p16 (.p16 (+.p16 x.im x.re) x.im) (-.p16 x.re x.im))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 (+.p16 x.im x.re) x.im) (-.p16 x.re x.im))) x.re (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)))

simplify3.6s

Counts

93 → 93

Iterations

Iter	Nodes
done	5085
3	2201
2	382
1	95
0	46

prune820.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize210.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.p16 (+.p16 x.re x.re) x.re)
0.1b	(*.p16 (+.p16 x.im x.re) x.im)
0.2b	(.p16 (.p16 (+.p16 x.im x.re) x.im) (-.p16 x.re x.im))
10.1b	(quire16-mul-add (posit16->quire16 (.p16 (.p16 (+.p16 x.im x.re) x.im) (-.p16 x.re x.im))) x.im (*.p16 (+.p16 x.re x.re) x.re))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

3.0ms	(*.p16 (+.p16 x.re x.re) x.re)
3.0ms	(*.p16 (+.p16 x.im x.re) x.im)
7.0ms	(.p16 (.p16 (+.p16 x.im x.re) x.im) (-.p16 x.re x.im))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 (+.p16 x.im x.re) x.im) (-.p16 x.re x.im))) x.im (*.p16 (+.p16 x.re x.re) x.re))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.1s

Counts

60 → 60

Iterations

Iter	Nodes
done	5090
3	1524
2	300
1	81
0	36

prune650.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize226.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.p16 (+.p16 x.re x.re) x.re)
0.1b	(*.p16 x.im (-.p16 x.re x.im))
0.2b	(.p16 (+.p16 x.im x.re) (.p16 x.im (-.p16 x.re x.im)))
10.1b	(quire16-mul-add (posit16->quire16 (.p16 (+.p16 x.im x.re) (.p16 x.im (-.p16 x.re x.im)))) x.im (*.p16 (+.p16 x.re x.re) x.re))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.p16 (+.p16 x.re x.re) x.re)
7.0ms	(*.p16 x.im (-.p16 x.re x.im))
19.0ms	(.p16 (+.p16 x.im x.re) (.p16 x.im (-.p16 x.re x.im)))
1.0ms	(quire16-mul-add (posit16->quire16 (.p16 (+.p16 x.im x.re) (.p16 x.im (-.p16 x.re x.im)))) x.im (*.p16 (+.p16 x.re x.re) x.re))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.2s

Counts

77 → 77

Iterations

Iter	Nodes
done	5040
3	2468
2	467
1	174
0	52

prune823.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes612.0ms

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

sample2.8s

Algorithm: halfpoints