Details

sample75.0ms

Algorithm: halfpoints

simplify1.2s

Counts

1 → 1

Iterations

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize362.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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:

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

simplify1.2s

Counts

69 → 69

Iterations

Iter	Nodes
done	2000
3	2000
2	374
1	97
0	46

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize293.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

3.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.im x.re))
5.0ms	(.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.re))
2.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.im)
3.0ms	(-.p16 (.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re 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 x.re x.im) (.p16 x.im x.re))
0.0ms	(.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.re))
0.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.im)
0.0ms	(-.p16 (.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.re)) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.im))

simplify1.1s

Counts

77 → 77

Iterations

Iter	Nodes
done	2000
3	2000
2	459
1	111
0	49

prune2.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize119.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

9.0ms	(+.p16 x.im (+.p16 x.im x.im))
4.0ms	(*.p16 x.im (+.p16 x.im (+.p16 x.im x.im)))
4.0ms	(.p16 x.re (-.p16 (.p16 x.re x.re) (*.p16 x.im (+.p16 x.im (+.p16 x.im x.im)))))
4.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im (+.p16 x.im (+.p16 x.im x.im))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.4s

Counts

76 → 76

Iterations

Iter	Nodes
done	2057
4	2057
3	1766
2	286
1	84
0	43

prune2.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize231.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

14.0ms	(*.p16 (+.p16 x.im x.im) x.im)
8.0ms	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))
8.0ms	(.p16 x.re (-.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (*.p16 (+.p16 x.im x.im) x.im)))
6.0ms	(-.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (.p16 (+.p16 x.im x.im) x.im))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify910.0ms

Counts

103 → 103

Iterations

Iter	Nodes
done	2006
3	2006
2	717
1	183
0	78

prune2.5s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes264.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
0	11

end0.0ms

sample3.0s

Algorithm: halfpoints