Details

sample120.0ms

Algorithm

halfpoints

Results

simplify280.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

280.0ms

(+.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))

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize304.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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

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))
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)

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

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.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 x.re x.re) (.p16 x.im x.im))

simplify1.8s

Counts

8 → 12

Calls

8 calls:

Slowest

535.0ms	(.p16 (-.p16 (.p16 (.p16 x.re x.re) (.p16 x.re x.re)) (.p16 (.p16 x.im x.im) (*.p16 x.im x.im))) x.im)
325.0ms	(+.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))
320.0ms	(+.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))
319.0ms	(+.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))
309.0ms	(+.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))

prune202.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize202.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.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 (.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)

rewrite14.0ms

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

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

simplify50.0ms

Counts

6 → 11

Calls

6 calls:

Slowest

44.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
1.0ms	(+.p16 x.re x.im)
1.0ms	(+.p16 x.re x.im)
1.0ms	(+.p16 x.re x.im)
1.0ms	(+.p16 x.re x.im)

prune175.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize213.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

5×	`distribute-rgt-in` `distribute-lft-in`
4×	`sub-neg`
3×	`*-commutative`
2×	`associate-+l+` `associate-+r+`
1×	`+-commutative` `associate-*r/` `p16-flip--`

Counts

4 → 15

Calls

4 calls:

Slowest

4.0ms	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))
4.0ms	(+.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (.p16 x.re (+.p16 x.re x.re)))
3.0ms	(*.p16 x.re (+.p16 x.re x.re))
2.0ms	(.p16 x.im (+.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (*.p16 x.re (+.p16 x.re x.re))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

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

simplify1.3s

Counts

15 → 19

Calls

15 calls:

Slowest

334.0ms	(.p16 x.im (+.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (*.p16 x.re (+.p16 x.re x.re))))
315.0ms	(.p16 x.im (+.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (*.p16 x.re (+.p16 x.re x.re))))
300.0ms	(.p16 x.im (+.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (*.p16 x.re (+.p16 x.re x.re))))
296.0ms	(.p16 x.im (+.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (*.p16 x.re (+.p16 x.re x.re))))
13.0ms	(.p16 (.p16 x.re (+.p16 x.re x.re)) x.im)

prune495.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize155.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 12

Calls

4 calls:

Slowest

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

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

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

simplify47.0ms

Counts

12 → 16

Calls

12 calls:

Slowest

8.0ms	(*.p16 (neg.p16 x.im) (+.p16 x.im x.re))
7.0ms	(*.p16 x.re (+.p16 x.im x.re))
6.0ms	(*.p16 (+.p16 x.im x.re) (neg.p16 x.im))
5.0ms	(*.p16 (+.p16 x.im x.re) x.re)
5.0ms	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))

prune228.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes155.0ms

Accuracy

-∞% (-63.6b remaining)

Error of 0.4b against oracle of 64.0b and baseline of 64.0b

bsearch1.0ms

end0.0ms

sample1.9s

Algorithm

halfpoints

Results