Details

sample118.0ms

Algorithm: halfpoints

simplify5.4s

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: 0.1b

localize334.0ms

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)
0.2b	(-.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))

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`
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:

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

69 → 69

Iterations

Iter	Nodes
done	5015
3	2062
2	374
1	97
0	46

prune745.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize272.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.1b	(*.p16 x.im (+.p16 x.re x.re))
0.2b	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
5.9b	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.im (+.p16 x.re x.re)) x.im)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

8.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
6.0ms	(*.p16 x.im (+.p16 x.re x.re))
11.0ms	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.im (+.p16 x.re 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 x.im (+.p16 x.re x.re))
0.0ms	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.im (+.p16 x.re x.re)) x.im)

simplify1.6s

Counts

61 → 61

Iterations

Iter	Nodes
done	5256
3	2314
2	314
1	84
0	42

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize236.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

18.0ms	(+.p16 (+.p16 x.im x.im) x.im)
17.0ms	(*.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im)
20.0ms	(.p16 x.re (-.p16 (.p16 x.re x.re) (*.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im)))
8.0ms	(-.p16 (.p16 x.re x.re) (.p16 (+.p16 (+.p16 x.im 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 (+.p16 x.im x.im) x.im) x.im)
0.0ms	(.p16 x.re (-.p16 (.p16 x.re x.re) (*.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im)))
0.0ms	(-.p16 (.p16 x.re x.re) (.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im))

simplify1.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
3	1222
2	235
1	74
0	42

prune733.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize181.0ms

Local error

Found 4 expressions with local error:

0.1b	(.p16 x.re (.p16 x.re x.re))
0.1b	(*.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im)
0.3b	(+.p16 (.p16 x.re (.p16 x.re x.re)) (.p16 x.re (neg.p16 (.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im))))
0.3b	(.p16 x.re (neg.p16 (.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

4.0ms	(.p16 x.re (.p16 x.re x.re))
8.0ms	(*.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im)
6.0ms	(+.p16 (.p16 x.re (.p16 x.re x.re)) (.p16 x.re (neg.p16 (.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im))))
3.0ms	(.p16 x.re (neg.p16 (.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify20.8s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
4	856
3	331
2	126
1	62
0	36

prune987.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes277.0ms

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

sample3.1s

Algorithm: halfpoints