Details

sample138.0ms

Algorithm

halfpoints

Results

simplify161.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

160.0ms

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize212.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 19

Calls

4 calls:

Slowest

13.0ms	(.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))
6.0ms	(-.p16 (.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))) (.p16 x.im (.p16 (+.p16 x.im x.im) x.re)))
4.0ms	(.p16 x.im (.p16 (+.p16 x.im x.im) x.re))
4.0ms	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

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

simplify5.9s

Counts

27 → 23

Calls

27 calls:

Slowest

1.1s	(-.p16 (.p16 (.p16 (+.p16 x.im x.re) (neg.p16 x.im)) x.re) (.p16 x.im (.p16 (+.p16 x.im x.im) x.re)))
1.1s	(-.p16 (.p16 (.p16 (neg.p16 x.im) (+.p16 x.im x.re)) x.re) (.p16 x.im (.p16 (+.p16 x.im x.im) x.re)))
837.0ms	(-.p16 (.p16 x.re (.p16 (+.p16 x.im x.re) (neg.p16 x.im))) (.p16 x.im (.p16 (+.p16 x.im x.im) x.re)))
750.0ms	(+.p16 (.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))) (.p16 x.im (.p16 (+.p16 x.im x.im) x.re)))
433.0ms	(.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 (.p16 x.re x.re) (.p16 x.im x.im))))

prune721.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize278.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 14

Calls

4 calls:

Slowest

10.0ms	(.p16 (.p16 x.re (+.p16 x.im x.re)) (-.p16 x.re x.im))
9.0ms	(-.p16 (.p16 (.p16 x.re (+.p16 x.im x.re)) (-.p16 x.re x.im)) (.p16 x.im (.p16 (+.p16 x.im x.im) x.re)))
9.0ms	(.p16 x.im (.p16 (+.p16 x.im x.im) x.re))
6.0ms	(*.p16 x.re (+.p16 x.im x.re))

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

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

simplify1.4s

Counts

20 → 18

Calls

20 calls:

Slowest

614.0ms	(-.p16 (.p16 (.p16 x.re (+.p16 x.im x.re)) (neg.p16 x.im)) (.p16 x.im (.p16 (+.p16 x.im x.im) x.re)))
334.0ms	(+.p16 (.p16 (.p16 x.re (+.p16 x.im x.re)) (-.p16 x.re x.im)) (.p16 x.im (.p16 (+.p16 x.im x.im) x.re)))
208.0ms	(-.p16 (.p16 (.p16 (.p16 x.re (+.p16 x.im x.re)) (-.p16 x.re x.im)) (.p16 (.p16 x.re (+.p16 x.im x.re)) (-.p16 x.re x.im))) (.p16 (.p16 x.im (.p16 (+.p16 x.im x.im) x.re)) (.p16 x.im (.p16 (+.p16 x.im x.im) x.re))))
75.0ms	(-.p16 (.p16 (neg.p16 x.im) (.p16 x.re (+.p16 x.im x.re))) (.p16 x.im (.p16 (+.p16 x.im x.im) x.re)))
55.0ms	(.p16 (.p16 x.re (+.p16 x.im x.re)) (-.p16 (.p16 x.re x.re) (.p16 x.im x.im)))

prune252.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize153.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 19

Calls

4 calls:

Slowest

10.0ms	(.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))
8.0ms	(-.p16 (.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))) (.p16 (.p16 x.im (+.p16 x.im x.im)) x.re))
7.0ms	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))
4.0ms	(.p16 (.p16 x.im (+.p16 x.im x.im)) x.re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

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

simplify3.6s

Counts

27 → 23

Calls

27 calls:

Slowest

1.1s	(-.p16 (.p16 (.p16 (+.p16 x.im x.re) (neg.p16 x.im)) x.re) (.p16 (.p16 x.im (+.p16 x.im x.im)) x.re))
847.0ms	(-.p16 (.p16 x.re (.p16 (+.p16 x.im x.re) (neg.p16 x.im))) (.p16 (.p16 x.im (+.p16 x.im x.im)) x.re))
690.0ms	(+.p16 (.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))) (.p16 (.p16 x.im (+.p16 x.im x.im)) x.re))
288.0ms	(.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 (.p16 x.re x.re) (.p16 x.im x.im))))
253.0ms	(-.p16 (.p16 (.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))) (.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))) (.p16 (.p16 (.p16 x.im (+.p16 x.im x.im)) x.re) (.p16 (.p16 x.im (+.p16 x.im x.im)) x.re)))

prune617.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize181.0ms

Local error

Found 4 expressions with local error:

0.9b	(/.p16 (.p16 (+.p16 x.re x.im) (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im))
0.3b	(-.p16 (.p16 x.re (/.p16 (.p16 (+.p16 x.re x.im) (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im))) (.p16 x.im (*.p16 (+.p16 x.im x.im) x.re)))
0.2b	(.p16 x.re (/.p16 (.p16 (+.p16 x.re x.im) (*.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im)))
0.2b	(.p16 x.im (.p16 (+.p16 x.im x.im) x.re))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 8

Calls

4 calls:

Slowest

15.0ms	(.p16 x.re (/.p16 (.p16 (+.p16 x.re x.im) (*.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im)))
7.0ms	(/.p16 (.p16 (+.p16 x.re x.im) (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im))
5.0ms	(.p16 x.im (.p16 (+.p16 x.im x.im) x.re))
4.0ms	(-.p16 (.p16 x.re (/.p16 (.p16 (+.p16 x.re x.im) (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im))) (.p16 x.im (*.p16 (+.p16 x.im x.im) 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) (-.p16 x.re x.im))) (+.p16 x.re x.im))
0.0ms	(-.p16 (.p16 x.re (/.p16 (.p16 (+.p16 x.re x.im) (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im))) (.p16 x.im (*.p16 (+.p16 x.im x.im) x.re)))
0.0ms	(.p16 x.re (/.p16 (.p16 (+.p16 x.re x.im) (*.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im)))
0.0ms	(.p16 x.im (.p16 (+.p16 x.im x.im) x.re))

simplify1.9s

Counts

11 → 12

Calls

11 calls:

Slowest

835.0ms	(.p16 x.re (.p16 (+.p16 x.re x.im) (*.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))))
207.0ms	(-.p16 (.p16 x.re (/.p16 (.p16 (+.p16 x.re x.im) (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im))) (.p16 x.im (*.p16 (+.p16 x.im x.im) x.re)))
198.0ms	(-.p16 (.p16 (.p16 x.re (/.p16 (.p16 (+.p16 x.re x.im) (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im))) (.p16 x.re (/.p16 (.p16 (+.p16 x.re x.im) (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im)))) (.p16 (.p16 x.im (.p16 (+.p16 x.im x.im) x.re)) (.p16 x.im (.p16 (+.p16 x.im x.im) x.re))))
175.0ms	(-.p16 (.p16 x.re (/.p16 (.p16 (+.p16 x.re x.im) (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im))) (.p16 x.im (*.p16 (+.p16 x.im x.im) x.re)))
168.0ms	(-.p16 (.p16 x.re (/.p16 (.p16 (+.p16 x.re x.im) (.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))) (+.p16 x.re x.im))) (.p16 x.im (*.p16 (+.p16 x.im x.im) x.re)))

prune217.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes209.0ms

Accuracy

-∞% (-63.6b remaining)

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

bsearch2.0ms

end0.0ms

sample2.5s

Algorithm

halfpoints

Results