Details

sample96.0ms

Algorithm

halfpoints

Results

simplify107.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

106.0ms

(-.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))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize265.0ms

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

rewrite18.0ms

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

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

simplify764.0ms

Counts

8 → 13

Calls

8 calls:

Slowest

361.0ms	(.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)
124.0ms	(-.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))
109.0ms	(-.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))
83.0ms	(-.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))
80.0ms	(-.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))

prune227.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize298.0ms

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)

rewrite24.0ms

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

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

simplify40.0ms

Counts

6 → 12

Calls

6 calls:

Slowest

33.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.re)
2.0ms	(+.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)

prune191.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize253.0ms

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 16

Calls

4 calls:

Slowest

18.0ms	(-.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)))
6.0ms	(*.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))

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.im) x.re)

simplify673.0ms

Counts

14 → 20

Calls

14 calls:

Slowest

179.0ms	(-.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)))
140.0ms	(-.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)))
136.0ms	(-.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)))
104.0ms	(-.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)))
22.0ms	(.p16 x.re (.p16 (+.p16 x.im x.re) (neg.p16 x.im)))

prune338.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize293.0ms

Local error

Found 4 expressions with local error:

0.4b	(-.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.im (.p16 (+.p16 x.im x.im) x.re))
0.1b	(*.p16 x.re (+.p16 x.im x.re))

rewrite16.0ms

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

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))
3.0ms	(*.p16 x.re (+.p16 x.im x.re))

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

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

simplify70.0ms

Counts

11 → 18

Calls

11 calls:

Slowest

18.0ms	(.p16 (neg.p16 x.im) (.p16 x.re (+.p16 x.im x.re)))
15.0ms	(.p16 (.p16 x.re (+.p16 x.im x.re)) x.re)
12.0ms	(.p16 (.p16 x.re (+.p16 x.im x.re)) (neg.p16 x.im))
11.0ms	(.p16 x.re (.p16 x.re (+.p16 x.im x.re)))
2.0ms	(-.p16 x.re x.im)

prune259.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes260.0ms

Accuracy

-∞% (-63.6b remaining)

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

bsearch1.0ms

end0.0ms

sample3.1s

Algorithm

halfpoints

Results