Details

sample69.0ms

Algorithm: halfpoints

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
7	4047
6	1485
5	622
4	223
3	106
2	51
1	21
0	11

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize242.0ms

Local error

Found 4 expressions with local error:

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)
0.3b	(-.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))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

8×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
7×	`associate-l`
6×	`p16-lft-identity-expand` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
4×	`associate--l+` `associate--r+`
3×	`associate-*l/` `p16-flip--`
2×	`associate--l-` `insert-quire-sub` `sub-neg` `*-commutative` `insert-quire-fdp-sub` `associate--r-` `difference-of-squares`

Counts

4 → 65

Calls

4 calls:

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

series0.0ms

Counts

4 → 4

Calls

4 calls:

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)
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))

simplify799.0ms

Counts

69 → 69

Iterations

Iter	Nodes
3	2023
2	329
1	92
0	46

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize282.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 x.re (+.p16 x.im x.im))
0.1b	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.2b	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
8.9b	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.re (+.p16 x.im x.im)) x.im)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`/p16-rgt-identity-expand`
8×	`distribute-rgt-in` `distribute-lft-in`
7×	`associate-r` `associate-*r/`
6×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
5×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
4×	`associate-*l/`
3×	`introduce-quire` `associate-l` `-p16-rgt-identity-expand` `*-commutative`
2×	`p16-flip--`

Counts

4 → 57

Calls

4 calls:

6.0ms	(*.p16 x.re (+.p16 x.im x.im))
4.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
4.0ms	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.re (+.p16 x.im x.im)) x.im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.p16 x.re (+.p16 x.im x.im))
0.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.0ms	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.re (+.p16 x.im x.im)) x.im)

simplify6.3s

Counts

61 → 61

Iterations

Iter	Nodes
4	7818
3	1341
2	300
1	81
0	42

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize243.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.2b	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
0.2b	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
8.9b	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)) x.im)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

8×	`/p16-rgt-identity-expand`
7×	`distribute-rgt-in` `distribute-lft-in` `+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`associate-*r/`
5×	`p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
4×	`associate-r` `associate-*l/`
3×	`associate-l`
2×	`associate-+l+` `associate-+r+` `p16-flip--` `*-commutative`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `p16-distribute-lft-out` `distribute-rgt-out` `insert-quire-fdp-add` `associate-+l-` `distribute-lft-out`

Counts

4 → 62

Calls

4 calls:

7.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
9.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
20.0ms	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)) x.im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.0ms	(+.p16 (.p16 x.im x.re) (.p16 x.im x.re))
0.0ms	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (+.p16 (.p16 x.im x.re) (.p16 x.im x.re)) x.im)

simplify25.5s

Counts

66 → 66

Iterations

Iter	Nodes
4	10963
3	1468
2	304
1	90
0	45

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize202.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.p16 x.im (+.p16 x.re x.re))
0.1b	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.2b	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
8.9b	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.im (+.p16 x.re x.re)) x.im)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`/p16-rgt-identity-expand`
8×	`distribute-rgt-in` `distribute-lft-in`
7×	`associate-r` `associate-*r/`
6×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
5×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
4×	`associate-*l/`
3×	`introduce-quire` `associate-l` `-p16-rgt-identity-expand` `*-commutative`
2×	`p16-flip--`

Counts

4 → 57

Calls

4 calls:

3.0ms	(*.p16 x.im (+.p16 x.re x.re))
4.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
4.0ms	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.im (+.p16 x.re x.re)) x.im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.p16 x.im (+.p16 x.re x.re))
0.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.0ms	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.im (+.p16 x.re x.re)) x.im)

simplify13.6s

Counts

61 → 61

Iterations

Iter	Nodes
4	12403
3	1587
2	296
1	79
0	40

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes367.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
1	11
0	11

end1.0ms

sample3.0s

Algorithm: halfpoints