Details

sample600.0ms

Algorithm

intervals

Results

86.0ms	260×	body	80	valid
84.0ms	56×	body	1280	valid
73.0ms	9×	body	160	valid
36.0ms	37×	body	640	valid
14.0ms	21×	body	320	valid

simplify2.9s

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize74.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(cos (+ (* (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

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×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

8.0ms	(* (atan2 x.im x.re) y.im)
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (atan2 x.im x.re) y.im)
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
229.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
4	2216
3	911
2	425
1	202
0	99

prune726.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.2b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

45.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
26.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
21.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
139.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
22.0ms	(* (atan2 x.im x.re) y.im)
73.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
4	4812
3	1753
2	685
1	297
0	137

prune653.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.2b

localize86.0ms

Local error

Found 4 expressions with local error:

23.0b	(posit16->real (real->posit16 (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite407.0ms

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×	`cos-sum` `remove-posit16`

Counts

4 → 50

Calls

4 calls:

0.0ms	(posit16->real (real->posit16 (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))))
375.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(posit16->real (real->posit16 (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))))
59.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
206.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.0s

Counts

62 → 62

Iterations

Iter	Nodes
done	5002
5	3593
4	1190
3	549
2	275
1	151
0	79

prune967.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

localize143.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite142.0ms

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×	`cos-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 43

Calls

4 calls:

17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
45.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
39.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series696.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
196.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
180.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
252.0ms	(cos (+ (* (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	3730
4	1185
3	540
2	265
1	141
0	70

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.2b

regimes678.0ms

Accuracy

62.4% (5.7b remaining)

Error of 9.5b against oracle of 3.7b and baseline of 19.0b

bsearch404.0ms

Steps

Iters	Range		Point
8	3.8921503778906023e-29	1.6235035004277907e-26	1.601505551461043e-26
8	-9.57290491357212e-281	-1.2897873214589416e-284	-1.8717104734621963e-281

simplify14.0ms

Iterations

Iter	Nodes
done	43
1	43
0	33

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.1s	1985×	body	1280	valid
2.0s	7951×	body	80	valid
1.8s	1414×	body	640	valid
339.0ms	637×	body	320	valid
94.0ms	275×	body	160	valid