Details

sample96.0ms

Algorithm

halfpoints

Results

simplify3.3s

Counts: 1 → 1

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize205.0ms

Local error

Found 4 expressions with local error:

0.4b	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))
0.2b	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
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))
0.1b	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

2×	`p16-flip--` `*-commutative` `difference-of-squares`
1×	`+-commutative` `sub-neg` `associate-l` `associate-*l/`

Counts

4 → 8

Calls

4 calls:

Slowest

5.0ms	(-.p16 (.p16 x.re x.re) (.p16 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))
3.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
2.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

0.0ms	(-.p16 (.p16 x.re x.re) (.p16 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 (.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)

simplify1.6s

Counts: 12 → 12

prune149.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize190.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-commutative`
2×	`associate-*l/` `p16-flip--`
1×	`+-commutative` `associate-r` `associate-*r/`

Counts

4 → 7

Calls

4 calls:

Slowest

6.0ms	(+.p16 (.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re 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.im) (.p16 (-.p16 x.re x.im) x.im))
3.0ms	(*.p16 (-.p16 x.re x.im) x.im)
2.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

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

simplify1.5s

Counts: 11 → 11

prune144.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize237.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

2×	`+-commutative` `*-commutative`
1×	`associate-l` `associate-l/` `associate-r/` `p16-flip--`

Counts

4 → 6

Calls

4 calls:

Slowest

11.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
10.0ms	(+.p16 (.p16 (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)) x.im) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re))
9.0ms	(.p16 (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)) x.im)
4.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.im x.re))

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

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

simplify897.0ms

Counts: 10 → 10

prune191.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize158.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

3×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
2×	`associate-+l+`
1×	`+-commutative` `associate-*l/` `p16-flip--`

Counts

4 → 11

Calls

4 calls:

Slowest

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

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

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

simplify1.6s

Counts: 15 → 15

prune141.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes215.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample3.3s

Algorithm

halfpoints

Results