Details

sample76.0ms

Algorithm: halfpoints

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3193
6	1358
5	610
4	230
3	107
2	49
1	20
0	11

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize323.0ms

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))

rewrite28.0ms

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

Counts

4 → 64

Calls

4 calls:

5.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
6.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
8.0ms	(+.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))
7.0ms	(-.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))

simplify1.2s

Counts

68 → 68

Iterations

Iter	Nodes
done	5007
3	1017
2	255
1	79
0	41

prune747.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize218.0ms

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))
0.2b	(.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
8.9b	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)) x.re)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`/p16-rgt-identity-expand`
7×	`distribute-rgt-in` `distribute-lft-in` `+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`associate-*r/`
5×	`p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
4×	`associate-r` `associate-*l/`
3×	`associate-l`
2×	`associate-+l+` `associate-+r+` `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 → 62

Calls

4 calls:

5.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
4.0ms	(+.p16 (.p16 x.im x.re) (.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 (.p16 x.im x.re) (.p16 x.im x.re)) 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 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 (.p16 x.im x.re) (.p16 x.im x.re)) x.re)

simplify1.3s

Counts

66 → 66

Iterations

Iter	Nodes
done	5025
3	1398
2	304
1	91
0	47

prune904.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize186.0ms

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

3.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
3.0ms	(*.p16 (-.p16 x.re x.im) x.im)
6.0ms	(.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.im))
6.0ms	(+.p16 (.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re 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.im) (*.p16 x.im x.re)) x.re)
0.0ms	(*.p16 (-.p16 x.re x.im) x.im)
0.0ms	(.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.im))
0.0ms	(+.p16 (.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.im)) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re))

simplify33.7s

Counts

73 → 73

Iterations

Iter	Nodes
done	5037
3	2443
2	282
1	85
0	39

prune688.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize204.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.p16 (+.p16 x.re x.re) x.re)
0.1b	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.2b	(+.p16 (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (.p16 (+.p16 x.re x.re) x.re))
0.3b	(.p16 x.im (+.p16 (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (*.p16 (+.p16 x.re x.re) x.re)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

7.0ms	(*.p16 (+.p16 x.re x.re) x.re)
8.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
8.0ms	(+.p16 (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (.p16 (+.p16 x.re x.re) x.re))
5.0ms	(.p16 x.im (+.p16 (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (*.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.re x.im) (+.p16 x.im x.re))
0.0ms	(+.p16 (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (.p16 (+.p16 x.re x.re) x.re))
0.0ms	(.p16 x.im (+.p16 (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (*.p16 (+.p16 x.re x.re) x.re)))

simplify1.9s

Counts

71 → 71

Iterations

Iter	Nodes
done	5014
3	2631
2	454
1	96
0	41

prune792.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes345.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
0	11

end0.0ms

sample2.6s

Algorithm: halfpoints