Details

sample110.0ms

Algorithm: halfpoints

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
8	4615
7	3127
6	1308
5	586
4	220
3	107
2	49
1	20
0	11

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize186.0ms

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.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))
0.4b	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))

rewrite20.0ms

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

Counts

4 → 68

Calls

4 calls:

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

simplify1.5s

Counts

72 → 72

Iterations

Iter	Nodes
done	5002
3	1021
2	224
1	84
0	46

prune882.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize217.0ms

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)))
9.0b	(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)

rewrite15.0ms

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:

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

simplify1.4s

Counts

66 → 66

Iterations

Iter	Nodes
done	5002
3	1464
2	290
1	91
0	47

prune963.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize263.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 x.re (+.p16 x.im x.im))
0.1b	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.2b	(.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
9.0b	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

rewrite14.0ms

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:

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

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.9s

Counts

61 → 61

Iterations

Iter	Nodes
done	5114
3	2290
2	304
1	81
0	40

prune761.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize254.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 x.re (+.p16 x.im x.im))
0.2b	(*.p16 x.im (-.p16 x.re x.im))
0.2b	(.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))
9.0b	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

3.0ms	(*.p16 x.re (+.p16 x.im x.im))
4.0ms	(*.p16 x.im (-.p16 x.re x.im))
13.0ms	(.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.3s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	1191
2	258
1	85
0	36

prune741.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

regimes210.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
0	9

end0.0ms

sample3.0s

Algorithm: halfpoints