Details

sample329.0ms

Algorithm

intervals

Results

156.0ms	79×	body	1280	valid
49.0ms	56×	body	640	valid
48.0ms	253×	body	80	valid
14.0ms	22×	body	320	valid
3.0ms	9×	body	160	valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
6	5698
5	805
4	195
3	82
2	53
1	31
0	19

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize68.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
30.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite40.0ms

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:

7.0ms	(* (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)))
18.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (atan2 x.im x.re) y.im)
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
231.0ms	(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
5	4090
4	1666
3	854
2	430
1	206
0	102

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.8b

localize133.0ms

Local error

Found 4 expressions with local error:

30.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite118.0ms

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)))
33.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
39.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series711.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
221.0ms	(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)))
244.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts

55 → 55

Iterations

Iter	Nodes
5	3217
4	1145
3	535
2	268
1	145
0	73

prune1.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.8b

localize136.0ms

Local error

Found 4 expressions with local error:

32.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

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)))
26.0ms	(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)))
32.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series802.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
197.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
196.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
190.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts

48 → 48

Iterations

Iter	Nodes
9	2033
8	983
7	594
6	438
5	294
4	171
3	112
2	85
1	65
0	43

prune1.3s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 20.8b

localize126.0ms

Local error

Found 4 expressions with local error:

32.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.3b	(sin (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
60.0b	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

rewrite48.0ms

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:

16.0ms	(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)))
15.0ms	(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)))))

series593.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
151.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
175.0ms	(sin (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
41.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify2.3s

Counts

48 → 48

Iterations

Iter	Nodes
9	3710
8	1450
7	786
6	547
5	365
4	232
3	158
2	120
1	99
0	69

prune1.9s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 20.7b

regimes945.0ms

Accuracy

76.8% (3.3b remaining)

Error of 22.4b against oracle of 19.1b and baseline of 33.2b

bsearch264.0ms

Steps

Iters	Range		Point
8	-8.737538094151048e-301	-8.73966273530909e-305	-8.85761317469186e-305

simplify12.0ms

Iterations

Iter	Nodes
2	39
1	39
0	30

end0.0ms

sample11.2s

Algorithm

intervals

Results

5.4s	2102×	body	1280	valid
2.4s	7927×	body	80	valid
2.1s	1414×	body	640	valid
532.0ms	509×	body	320	valid
157.0ms	51×	body	2560	valid
144.0ms	249×	body	160	valid