Details

sample78.0ms

Algorithm: halfpoints

simplify865.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
7	2002
6	1308
5	586
4	220
3	107
2	49
1	20
0	11

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize209.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

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

Counts

4 → 66

Calls

4 calls:

2.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
5.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.im x.re))
6.0ms	(+.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))
5.0ms	(-.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.re)
0.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.im 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))

simplify950.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	2022
4	2022
3	999
2	260
1	84
0	45

prune728.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize298.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (.p16 x.im (-.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 x.re x.im))
7.7b	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))) (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)) x.re)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

5.0ms	(.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))
4.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
4.0ms	(*.p16 x.im (-.p16 x.re x.im))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.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.im (-.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 x.re x.im))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))) (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)) x.re)

simplify1.1s

Counts

63 → 63

Iterations

Iter	Nodes
done	2158
4	2158
3	1444
2	292
1	96
0	44

prune804.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize426.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
0.2b	(*.p16 x.im (+.p16 x.im x.re))
0.9b	(/.p16 (.p16 (-.p16 x.re x.im) (.p16 x.im (+.p16 x.im x.re))) (+.p16 x.re x.im))
7.7b	(quire16-mul-add (posit16->quire16 (.p16 (/.p16 (.p16 (-.p16 x.re x.im) (.p16 x.im (+.p16 x.im x.re))) (+.p16 x.re x.im)) (+.p16 x.im x.re))) (+.p16 (.p16 x.im x.re) (*.p16 x.im x.re)) x.re)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

7.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
14.0ms	(*.p16 x.im (+.p16 x.im x.re))
15.0ms	(/.p16 (.p16 (-.p16 x.re x.im) (.p16 x.im (+.p16 x.im x.re))) (+.p16 x.re x.im))
1.0ms	(quire16-mul-add (posit16->quire16 (.p16 (/.p16 (.p16 (-.p16 x.re x.im) (.p16 x.im (+.p16 x.im x.re))) (+.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.im x.re) (.p16 x.im x.re))
0.0ms	(*.p16 x.im (+.p16 x.im x.re))
0.0ms	(/.p16 (.p16 (-.p16 x.re x.im) (.p16 x.im (+.p16 x.im x.re))) (+.p16 x.re x.im))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (/.p16 (.p16 (-.p16 x.re x.im) (.p16 x.im (+.p16 x.im x.re))) (+.p16 x.re x.im)) (+.p16 x.im x.re))) (+.p16 (.p16 x.im x.re) (*.p16 x.im x.re)) x.re)

simplify1.3s

Counts

60 → 60

Iterations

Iter	Nodes
done	2002
4	2002
3	1621
2	339
1	88
0	40

prune792.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize302.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.p16 x.im (+.p16 x.im x.re))
0.3b	(.p16 (/.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (.p16 x.im (+.p16 x.im x.re)))
0.8b	(/.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
7.7b	(quire16-mul-add (posit16->quire16 (.p16 (.p16 (/.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (.p16 x.im (+.p16 x.im x.re))) (+.p16 x.im x.re))) (+.p16 (.p16 x.im x.re) (*.p16 x.im x.re)) x.re)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

19×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
18×	`p16-times-frac`
13×	`associate-l`
9×	`/p16-rgt-identity-expand`
7×	`distribute-rgt-in` `distribute-lft-in`
5×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
4×	`associate-r` `associate-*r/`
3×	`associate-/r` `introduce-quire` `-p16-rgt-identity-expand` `associate-/l`
2×	`associate-/r/` `*-commutative` `associate-/l/`
1×	`associate-*l/` `p16-flip--`

Counts

4 → 75

Calls

4 calls:

3.0ms	(*.p16 x.im (+.p16 x.im x.re))
6.0ms	(.p16 (/.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (.p16 x.im (+.p16 x.im x.re)))
5.0ms	(/.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 (/.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (.p16 x.im (+.p16 x.im x.re))) (+.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 x.im (+.p16 x.im x.re))
0.0ms	(.p16 (/.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (.p16 x.im (+.p16 x.im x.re)))
0.0ms	(/.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 (/.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)) (.p16 x.im (+.p16 x.im x.re))) (+.p16 x.im x.re))) (+.p16 (.p16 x.im x.re) (*.p16 x.im x.re)) x.re)

simplify1.5s

Counts

79 → 79

Iterations

Iter	Nodes
done	2019
3	2019
2	580
1	131
0	46

prune792.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes220.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
0	13

end0.0ms

sample3.2s

Algorithm: halfpoints