Details

sample77.0ms

Algorithm: halfpoints

simplify1.9s

Counts

1 → 1

Iterations

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize241.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
0.2b	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
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))
0.3b	(-.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`
3×	`associate-*l/`
2×	`associate-+l+` `associate-+r+` `associate--l+` `p16-flip--` `*-commutative` `associate--r+` `difference-of-squares`
1×	`associate--l-` `+-commutative` `insert-quire-sub` `associate-+r-` `sub-neg` `insert-quire-add` `insert-quire-fdp-add` `associate-+l-` `insert-quire-fdp-sub` `associate--r-`

Counts

4 → 64

Calls

4 calls:

5.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
4.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
7.0ms	(+.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))
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.re) (*.p16 x.im x.im)) x.im)
0.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
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))

simplify15.4s

Counts

68 → 68

Iterations

Iter	Nodes
4	11141
3	923
2	204
1	74
0	41

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize273.0ms

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)))
8.0b	(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)

rewrite42.0ms

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:

24.0ms	(*.p16 x.re (+.p16 x.im x.im))
8.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
8.0ms	(.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
1.0ms	(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)

simplify7.0s

Counts

61 → 61

Iterations

Iter	Nodes
4	8298
3	1351
2	283
1	81
0	42

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize181.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

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

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.4s

Counts

71 → 71

Iterations

Iter	Nodes
4	5618
3	1005
2	228
1	83
0	40

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize201.0ms

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

7.0b

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

rewrite6.0ms

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))

2.0ms

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

0.0ms

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

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

0.0ms

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

simplify1.1s

Counts

40 → 40

Iterations

Iter	Nodes
4	2923
3	482
2	137
1	53
0	29

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes274.0ms

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	10
0	10

end0.0ms

sample2.9s

Algorithm: halfpoints