Details

sample911.0ms

Algorithm

intervals

Results

537.0ms	36×	body	640	valid
137.0ms	250×	body	80	valid
135.0ms	61×	body	1280	valid
16.0ms	15×	body	320	valid
6.0ms	9×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1115
4	236
3	85
2	53
1	31
0	19

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize92.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.im)
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite60.0ms

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)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (atan2 x.im x.re) y.im)
62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
228.0ms	(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
done	5000
3	2607
2	559
1	207
0	102

prune725.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.5b

localize110.0ms

Local error

Found 4 expressions with local error:

31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite69.0ms

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:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms	(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)))

series693.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
206.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
213.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
225.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
4	1888
3	657
2	295
1	146
0	73

prune674.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.5b

localize116.0ms

Local error

Found 4 expressions with local error:

35.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite131.0ms

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:

28.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.0ms	(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)))
33.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series806.0ms

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)))
226.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
204.0ms	(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)))

simplify4.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
5	4295
4	474
3	142
2	87
1	66
0	43

prune657.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.5b

localize91.0ms

Local error

Found 4 expressions with local error:

31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite84.0ms

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:

11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
27.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series647.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
224.0ms	(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)))
174.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
4	1888
3	657
2	295
1	146
0	73

prune721.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 17.5b

regimes739.0ms

Accuracy

77.2% (3.2b remaining)

Error of 22.3b against oracle of 19.1b and baseline of 33.3b

bsearch318.0ms

Steps

Iters	Range		Point
8	-6.28539424680076e-307	3.3383700148803893e-307	-1.91205330543206e-310

simplify11.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample11.8s

Algorithm

intervals

Results

4.8s	2169×	body	1280	valid
2.6s	7948×	body	80	valid
2.4s	1439×	body	640	valid
1.0s	537×	body	320	valid
229.0ms	248×	body	160	valid
207.0ms	53×	body	2560	valid