Details

sample90.0ms

Algorithm

halfpoints

Results

simplify275.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

275.0ms

(+.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))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize305.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

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

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

simplify1.8s

Counts

11 → 12

Calls

11 calls:

Slowest

735.0ms	(.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)
288.0ms	(+.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))
278.0ms	(+.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))
220.0ms	(+.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))
204.0ms	(+.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))

prune210.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize301.0ms

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 5

Calls

4 calls:

Slowest

10.0ms	(+.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))
7.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.im x.re))
5.0ms	(*.p16 (-.p16 x.re x.im) x.im)
5.0ms	(.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 x.im 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) x.im)

simplify79.0ms

Counts

5 → 9

Calls

5 calls:

Slowest

48.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
11.0ms	(*.p16 (-.p16 x.re x.im) x.im)
10.0ms	(*.p16 (-.p16 x.re x.im) x.im)
4.0ms	(*.p16 (-.p16 x.re x.im) x.im)
4.0ms	(*.p16 (-.p16 x.re x.im) x.im)

prune101.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize225.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 6

Calls

4 calls:

Slowest

5.0ms	(+.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))
4.0ms	(.p16 (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im)) x.im)
3.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.im x.re))
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 (+.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.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) (.p16 x.im x.re))

simplify564.0ms

Counts

10 → 10

Calls

10 calls:

Slowest

537.0ms	(.p16 (.p16 (+.p16 x.re x.im) (-.p16 (.p16 x.re x.re) (.p16 x.im x.im))) x.im)
11.0ms	(*.p16 (-.p16 x.re x.im) x.im)
2.0ms	(-.p16 x.re x.im)
2.0ms	(-.p16 x.re x.im)
2.0ms	(-.p16 x.re x.im)

prune172.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize199.0ms

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))))
0.2b	(+.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))

simplify1.9s

Counts

21 → 19

Calls

21 calls:

Slowest

522.0ms	(.p16 x.im (+.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (*.p16 x.re (+.p16 x.re x.re))))
405.0ms	(.p16 x.im (+.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (*.p16 x.re (+.p16 x.re x.re))))
354.0ms	(.p16 x.im (+.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (*.p16 x.re (+.p16 x.re x.re))))
319.0ms	(.p16 x.im (+.p16 (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)) (*.p16 x.re (+.p16 x.re x.re))))
46.0ms	(.p16 (+.p16 x.im x.re) (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)))

prune256.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes195.0ms

Accuracy

-∞% (-63.6b remaining)

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

bsearch1.0ms

end0.0ms

sample2.7s

Algorithm

halfpoints

Results