Details

sample676.0ms

Algorithm

intervals

Results

52.0ms	61×	body	1280	valid
34.0ms	257×	body	80	valid
15.0ms	30×	body	640	valid
6.0ms	15×	body	320	valid
2.0ms	8×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	808
4	197
3	82
2	53
1	31
0	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize89.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.im)
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

5.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.im)
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
182.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
4	2127
3	906
2	432
1	207
0	102

prune729.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.2b

localize115.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`sin-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 43

Calls

4 calls:

12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
16.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
24.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
184.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
183.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
205.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.9s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
5	3634
4	1189
3	531
2	270
1	146
0	73

prune755.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 15.2b

localize87.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`sin-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 43

Calls

4 calls:

12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
15.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
24.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series662.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
232.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
195.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
193.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.9s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
5	3634
4	1189
3	531
2	270
1	146
0	73

prune674.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 15.2b

localize160.0ms

Local error

Found 4 expressions with local error:

31.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(sin (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
60.2b	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`sin-sum`
1×	`remove-posit16`

Counts

4 → 36

Calls

4 calls:

29.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
15.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
23.0ms	(sin (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
1.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

series617.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
165.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
202.0ms	(sin (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
70.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify3.5s

Counts

48 → 48

Iterations

Iter	Nodes
done	5011
9	4248
8	2354
7	1406
6	1087
5	489
4	279
3	177
2	122
1	100
0	69

prune833.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 15.2b

regimes1.0s

Accuracy

75.7% (3.3b remaining)

Error of 22.3b against oracle of 19.0b and baseline of 32.5b

bsearch190.0ms

Steps

Iters	Range		Point
9	-3.624048073274082e-307	9.672750817997472e-303	4.11803379523495e-310

simplify11.0ms

Iterations

Iter	Nodes
done	39
1	39
0	30

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.5s	2190×	body	1280	valid
1.8s	1392×	body	640	valid
1.8s	7957×	body	80	valid
745.0ms	590×	body	320	valid
133.0ms	247×	body	160	valid
133.0ms	56×	body	2560	valid