Details

sample523.0ms

Algorithm

intervals

Results

172.0ms	81×	body	1280	valid
133.0ms	259×	body	80	valid
60.0ms	39×	body	640	valid
17.0ms	16×	body	320	valid
8.0ms	2×	body	2560	valid
6.0ms	8×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2059
6	2059
5	808
4	197
3	82
2	53
1	31
0	19

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize79.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite55.0ms

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:

11.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(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)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (atan2 x.im x.re) y.im)
59.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
260.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	2004
4	2004
3	906
2	432
1	207
0	102

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.4b

localize94.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite88.0ms

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)))
34.0ms	(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)))

series700.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
195.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
249.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
203.0ms	(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
done	2002
5	2002
4	1189
3	531
2	270
1	146
0	73

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 16.4b

localize91.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0b	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
0.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
202.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
21.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

simplify1.4s

Counts

62 → 62

Iterations

Iter	Nodes
done	2040
5	2040
4	1311
3	616
2	308
1	159
0	85

prune2.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.4b

localize121.0ms

Local error

Found 4 expressions with local error:

33.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0b	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.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:

15.0ms	(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)))
16.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
0.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

series590.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(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)))
224.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
24.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

simplify1.4s

Counts

48 → 48

Iterations

Iter	Nodes
done	2000
7	2000
6	1949
5	690
4	348
3	211
2	125
1	79
0	55

prune1.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.4b

regimes1.1s

Accuracy

77.4% (3.0b remaining)

Error of 22.3b against oracle of 19.3b and baseline of 32.4b

bsearch299.0ms

Steps

Iters	Range		Point
8	-6.245387472968191e-307	2.5049244080050127e-307	-4.1355045148069e-310

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample11.5s

Algorithm

intervals

Results

4.7s	2254×	body	1280	valid
2.7s	1375×	body	640	valid
2.3s	7983×	body	80	valid
1.1s	545×	body	320	valid
149.0ms	52×	body	2560	valid
138.0ms	223×	body	160	valid