Details

sample541.0ms

Algorithm

intervals

Results

176.0ms	61×	body	1280	valid
85.0ms	257×	body	80	valid
40.0ms	30×	body	640	valid
14.0ms	15×	body	320	valid
5.0ms	8×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize65.0ms

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)))

rewrite50.0ms

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:

6.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.im)
48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
214.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

72 → 72

Iterations

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

prune680.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.2b

localize103.0ms

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)))

rewrite78.0ms

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:

8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0ms	(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)))
26.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series629.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
201.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
211.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
168.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.0s

Counts

55 → 55

Iterations

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

prune817.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 15.2b

localize84.0ms

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)))

rewrite82.0ms

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)))
31.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
22.0ms	(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)))

series592.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
160.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
189.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
202.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.8s

Counts

55 → 55

Iterations

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

prune681.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 15.2b

localize131.0ms

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)))))

rewrite74.0ms

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:

27.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
16.0ms	(sin (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
0.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

series658.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
180.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
208.0ms	(sin (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
45.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify3.9s

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

prune718.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 15.2b

regimes1.1s

Accuracy

75.7% (3.3b remaining)

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

bsearch314.0ms

Steps

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

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample11.4s

Algorithm

intervals

Results

4.6s	2190×	body	1280	valid
3.3s	7957×	body	80	valid
2.0s	1392×	body	640	valid
631.0ms	590×	body	320	valid
225.0ms	56×	body	2560	valid
138.0ms	247×	body	160	valid