Details

sample130.0ms

Algorithm

halfpoints

Results

simplify116.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

116.0ms

(-.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))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize172.0ms

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))

rewrite20.0ms

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

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

simplify4.7s

Counts

27 → 23

Calls

27 calls:

Slowest

814.0ms	(-.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)))
782.0ms	(-.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)))
719.0ms	(-.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)))
699.0ms	(+.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)))
347.0ms	(.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 (.p16 x.re x.re) (.p16 x.im x.im))))

prune421.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize169.0ms

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))

rewrite24.0ms

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

9.0ms	(*.p16 x.re (+.p16 x.im x.re))
5.0ms	(.p16 (.p16 x.re (+.p16 x.im x.re)) (-.p16 x.re x.im))
4.0ms	(-.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)))
4.0ms	(.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 (+.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))

simplify2.3s

Counts

20 → 18

Calls

20 calls:

Slowest

758.0ms	(-.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))))
692.0ms	(-.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)))
479.0ms	(+.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)))
109.0ms	(-.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)))
98.0ms	(.p16 (.p16 x.re (+.p16 x.im x.re)) (-.p16 (.p16 x.re x.re) (.p16 x.im x.im)))

prune501.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize312.0ms

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))

rewrite50.0ms

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

21.0ms	(.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))
10.0ms	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))
10.0ms	(-.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))
8.0ms	(.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 (+.p16 x.im x.re) (-.p16 x.re x.im))
0.0ms	(.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))

simplify3.5s

Counts

27 → 23

Calls

27 calls:

Slowest

1.1s	(-.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))
873.0ms	(-.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))
410.0ms	(+.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))
385.0ms	(-.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)))
249.0ms	(.p16 x.re (.p16 (+.p16 x.im x.re) (-.p16 (.p16 x.re x.re) (.p16 x.im x.im))))

prune480.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize251.0ms

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))

rewrite23.0ms

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

8.0ms	(.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))
4.0ms	(.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))

simplify2.1s

Counts

11 → 12

Calls

11 calls:

Slowest

933.0ms	(.p16 x.re (.p16 (+.p16 x.re x.im) (*.p16 (+.p16 x.re x.im) (-.p16 x.re x.im))))
245.0ms	(-.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)))
239.0ms	(-.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)))
235.0ms	(-.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)))
211.0ms	(-.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))))

prune140.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes178.0ms

Accuracy

-∞% (-63.6b remaining)

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

bsearch3.0ms

end0.0ms

sample2.8s

Algorithm

halfpoints

Results