Details

sample75.0ms

Algorithm: halfpoints

simplify1.6s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize249.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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:

3.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.re)
2.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.im)
4.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))
11.0ms	(-.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.re) (*.p16 x.im x.im)) x.re)
0.0ms	(.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))
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))

simplify1.1s

Counts

69 → 69

Iterations

Iter	Nodes
done	2000
3	2000
2	368
1	96
0	46

prune801.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize282.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.p16 (.p16 x.re x.im) (.p16 x.re x.im))
0.1b	(*.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))
0.2b	(.p16 x.re (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)))
10.9b	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)))) (+.p16 (.p16 x.re x.im) (.p16 x.re x.im)) x.im)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

7.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.re x.im))
8.0ms	(*.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))
10.0ms	(.p16 x.re (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)))) (+.p16 (.p16 x.re x.im) (.p16 x.re x.im)) x.im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.4s

Counts

78 → 78

Iterations

Iter	Nodes
done	2005
3	2005
2	344
1	125
0	57

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize348.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 x.im (+.p16 x.re x.re))
0.1b	(*.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))
0.2b	(.p16 x.re (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)))
10.9b	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)))) (*.p16 x.im (+.p16 x.re x.re)) x.im)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

6.0ms	(*.p16 x.im (+.p16 x.re x.re))
9.0ms	(*.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))
11.0ms	(.p16 x.re (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)))
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)))) (*.p16 x.im (+.p16 x.re x.re)) x.im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.8s

Counts

73 → 73

Iterations

Iter	Nodes
done	2072
3	2072
2	364
1	114
0	50

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize309.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 x.im (+.p16 x.re x.re))
0.1b	(*.p16 x.re (+.p16 x.re x.im))
0.2b	(.p16 (.p16 x.re (+.p16 x.re x.im)) (-.p16 x.re x.im))
10.9b	(quire16-mul-sub (posit16->quire16 (.p16 (.p16 x.re (+.p16 x.re x.im)) (-.p16 x.re x.im))) (*.p16 x.im (+.p16 x.re x.re)) x.im)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

6.0ms	(*.p16 x.im (+.p16 x.re x.re))
5.0ms	(*.p16 x.re (+.p16 x.re x.im))
9.0ms	(.p16 (.p16 x.re (+.p16 x.re x.im)) (-.p16 x.re x.im))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 (.p16 x.re (+.p16 x.re x.im)) (-.p16 x.re x.im))) (*.p16 x.im (+.p16 x.re x.re)) x.im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.2s

Counts

57 → 57

Iterations

Iter	Nodes
done	2003
3	2003
2	288
1	77
0	33

prune794.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.1b

regimes335.0ms

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

sample2.7s

Algorithm: halfpoints