Details

sample84.0ms

Algorithm: halfpoints

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
7	4047
6	1485
5	622
4	223
3	106
2	51
1	21
0	11

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize227.0ms

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 (.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))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
5×	`p16-lft-identity-expand` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
4×	`associate-l` `associate--l+` `associate--r+`
3×	`p16-flip--`
2×	`associate--l-` `insert-quire-sub` `associate-+l+` `associate-+r+` `sub-neg` `associate-*l/` `insert-quire-fdp-sub` `associate--r-` `difference-of-squares`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `*-commutative` `insert-quire-fdp-add` `associate-+l-`

Counts

4 → 69

Calls

4 calls:

5.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.im x.re))
4.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.re)
3.0ms	(-.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))
4.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im 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 (.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))

simplify38.4s

Counts

73 → 73

Iterations

Iter	Nodes
4	25543
3	1953
2	356
1	101
0	51

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize197.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
10×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
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`
3×	`sub-neg` `associate-l/` `associate-r/` `p16-flip--` `*-commutative` `associate--r-`
2×	`associate--r+`
1×	`associate--l-` `insert-quire-sub` `insert-quire-fdp-sub`

Counts

4 → 83

Calls

4 calls:

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

simplify1.7s

Counts

87 → 87

Iterations

Iter	Nodes
3	3133
2	476
1	118
0	60

prune3.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize230.0ms

Local error

Found 3 expressions with local error:

0.1b

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

0.2b

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

6.9b

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 37

Calls

3 calls:

4.0ms

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

4.0ms

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

1.0ms

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

series0.0ms

Counts

3 → 3

Calls

3 calls:

0.0ms

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

0.0ms

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

0.0ms

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

simplify1.1s

Counts

40 → 40

Iterations

Iter	Nodes
4	2741
3	562
2	148
1	53
0	29

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize251.0ms

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

rewrite32.0ms

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:

5.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.im)
11.0ms	(.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.re))
6.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.im x.re))
7.0ms	(-.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 (.p16 x.re x.im) (*.p16 x.im x.re)) x.im)
0.0ms	(.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) 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 (-.p16 x.re x.im) x.re)) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.im))

simplify2.8s

Counts

77 → 77

Iterations

Iter	Nodes
3	2880
2	443
1	109
0	49

prune1.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes263.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
1	12
0	12

end0.0ms

sample3.2s

Algorithm: halfpoints