Details

sample86.0ms

Algorithm

halfpoints

Results

simplify105.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

105.0ms

(-.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))

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize321.0ms

Local error

Found 4 expressions with local error:

0.4b	(-.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))
0.3b	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))
0.3b	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.re)
0.2b	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.im)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 9

Calls

4 calls:

Slowest

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

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

simplify798.0ms

Counts

8 → 13

Calls

8 calls:

Slowest

386.0ms	(.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.re)
142.0ms	(-.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))
90.0ms	(-.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))
89.0ms	(-.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))
85.0ms	(-.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))

prune303.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize330.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 8

Calls

4 calls:

Slowest

11.0ms	(.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.re))
6.0ms	(-.p16 (.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.re)) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.im))
5.0ms	(*.p16 (-.p16 x.re x.im) x.re)
5.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.im)

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

simplify57.0ms

Counts

6 → 12

Calls

6 calls:

Slowest

46.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.re)
2.0ms	(+.p16 x.re x.im)
2.0ms	(+.p16 x.re x.im)
2.0ms	(+.p16 x.re x.im)
2.0ms	(+.p16 x.re x.im)

prune237.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize296.0ms

Local error

Found 4 expressions with local error:

0.4b	(-.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)))
0.3b	(.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))

rewrite41.0ms

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

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

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

0.0ms	(-.p16 (.p16 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.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))

simplify957.0ms

Counts

17 → 23

Calls

17 calls:

Slowest

211.0ms	(-.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)))
207.0ms	(-.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)))
186.0ms	(-.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)))
180.0ms	(-.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)))
27.0ms	(.p16 (.p16 (neg.p16 x.im) (+.p16 x.im x.re)) x.re)

prune740.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize167.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

6×	`p16-distribute-lft-out` `distribute-lft-out`
3×	`sub-neg` `distribute-rgt-out`
2×	`+-commutative` `p16-flip--`
1×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-r/` `-commutative` `associate--r+`

Counts

4 → 19

Calls

4 calls:

Slowest

45.0ms	(.p16 x.re (-.p16 (.p16 x.re x.re) (+.p16 (.p16 x.im x.im) (+.p16 (.p16 x.im x.im) (*.p16 x.im x.im)))))
31.0ms	(-.p16 (.p16 x.re x.re) (+.p16 (.p16 x.im x.im) (+.p16 (.p16 x.im x.im) (.p16 x.im x.im))))
14.0ms	(+.p16 (.p16 x.im x.im) (+.p16 (.p16 x.im x.im) (*.p16 x.im x.im)))
8.0ms	(+.p16 (.p16 x.im x.im) (.p16 x.im x.im))

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

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

simplify1.8s

Counts

18 → 23

Calls

18 calls:

Slowest

442.0ms	(.p16 x.re (-.p16 (.p16 x.re x.re) (+.p16 (.p16 x.im x.im) (+.p16 (.p16 x.im x.im) (*.p16 x.im x.im)))))
429.0ms	(.p16 x.re (-.p16 (.p16 x.re x.re) (+.p16 (.p16 x.im x.im) (+.p16 (.p16 x.im x.im) (*.p16 x.im x.im)))))
422.0ms	(.p16 x.re (-.p16 (.p16 x.re x.re) (+.p16 (.p16 x.im x.im) (+.p16 (.p16 x.im x.im) (*.p16 x.im x.im)))))
416.0ms	(.p16 x.re (-.p16 (.p16 x.re x.re) (+.p16 (.p16 x.im x.im) (+.p16 (.p16 x.im x.im) (*.p16 x.im x.im)))))
31.0ms	(+.p16 (.p16 x.re x.re) (+.p16 (.p16 x.im x.im) (+.p16 (.p16 x.im x.im) (.p16 x.im x.im))))

prune326.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes394.0ms

Accuracy

-∞% (-63.6b remaining)

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

bsearch2.0ms

end0.0ms

sample3.2s

Algorithm

halfpoints

Results