Details

sample116.0ms

Algorithm: halfpoints

simplify4.5s

Counts

1 → 1

Iterations

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

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize204.0ms

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))

rewrite41.0ms

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:

7.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.im x.re))
7.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.re)
23.0ms	(-.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))
3.0ms	(-.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))

simplify40.3s

Counts

73 → 73

Iterations

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

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize220.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (+.p16 x.im x.im) x.re)
0.1b	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.2b	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
6.8b	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 (+.p16 x.im x.im) x.re) x.im)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

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

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify10.8s

Counts

59 → 59

Iterations

Iter	Nodes
4	9550
3	1200
2	267
1	79
0	40

prune2.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize201.0ms

Local error

Found 4 expressions with local error:

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)
0.2b	(+.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))

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:

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 x.re x.im) (.p16 x.im x.re))
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 (-.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 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	2928
2	453
1	109
0	49

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize212.0ms

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

rewrite34.0ms

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:

6.0ms	(*.p16 (+.p16 x.im x.im) x.im)
7.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
16.0ms	(-.p16 (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (.p16 (+.p16 x.im x.im) x.im))
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)))

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

simplify1.8s

Counts

87 → 87

Iterations

Iter	Nodes
3	3119
2	457
1	121
0	60

prune4.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes402.0ms

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
1	11
0	11

end0.0ms

sample3.4s

Algorithm: halfpoints