Details

sample292.0ms

Algorithm

intervals

Results

83.0ms	66×	body	1280	valid
76.0ms	42×	body	640	valid
48.0ms	253×	body	80	valid
6.0ms	11×	body	320	valid
3.0ms	8×	body	160	valid
2.0ms	1×	body	2560	valid

simplify3.1s

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: 32.3b

localize92.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (atan2 x.im x.re) y.re)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite57.0ms

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.re)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (atan2 x.im x.re) y.re)
48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
236.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
4	2040
3	860
2	413
1	203
0	100

prune589.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.7b

localize101.0ms

Local error

Found 4 expressions with local error:

24.4b	(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

10.0ms	(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.8s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
5	3766
4	1209
3	551
2	265
1	130
0	60

prune795.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.7b

localize103.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite79.0ms

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)))
28.0ms	(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 (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series683.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
209.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
217.0ms	(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)))

simplify3.4s

Counts

55 → 55

Iterations

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

prune845.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.7b

localize159.0ms

Local error

Found 4 expressions with local error:

30.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.5b	(sin (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
59.7b	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

rewrite72.0ms

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:

36.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
20.0ms	(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)))
1.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

series718.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
216.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
223.0ms	(sin (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
66.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify3.7s

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

prune936.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.7b

regimes856.0ms

Accuracy

75.6% (3.3b remaining)

Error of 22.9b against oracle of 19.6b and baseline of 33.1b

bsearch180.0ms

Steps

Iters	Range		Point
8	-2.439564962497264e-306	1.2873264571255324e-307	-4.2640896224449e-310

simplify24.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.7s	2232×	body	1280	valid
2.1s	7967×	body	80	valid
1.8s	1424×	body	640	valid
350.0ms	584×	body	320	valid
110.0ms	45×	body	2560	valid
89.0ms	244×	body	160	valid