Details

sample484.0ms

Algorithm

intervals

Results

119.0ms	61×	body	1280	valid
99.0ms	36×	body	640	valid
56.0ms	250×	body	80	valid
9.0ms	15×	body	320	valid
4.0ms	9×	body	160	valid

simplify4.2s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize304.0ms

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)))

rewrite196.0ms

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:

31.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
87.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series748.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (atan2 x.im x.re) y.im)
61.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
87.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
555.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify5.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
4	2214
3	916
2	421
1	207
0	102

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.7b

localize473.0ms

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)))

rewrite213.0ms

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:

34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
70.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
50.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series1.4s

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
442.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
451.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
462.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify7.4s

Counts

55 → 55

Iterations

Iter	Nodes
done	5002
5	3680
4	1177
3	538
2	270
1	146
0	73

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.7b

localize978.0ms

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)))

rewrite187.0ms

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:

53.0ms	(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)))
41.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
52.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series1.9s

Counts

4 → 12

Calls

4 calls:

468.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
485.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
513.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
466.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify8.2s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
9	2814
8	1950
7	1241
6	996
5	407
4	215
3	128
2	87
1	66
0	43

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.7b

localize839.0ms

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)))

rewrite209.0ms

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:

53.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
73.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
43.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
40.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series1.7s

Counts

4 → 12

Calls

4 calls:

436.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
471.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
383.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
423.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify8.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
9	2814
8	1950
7	1241
6	996
5	407
4	215
3	128
2	87
1	66
0	43

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.7b

regimes1.7s

Accuracy

77.8% (3.2b remaining)

Error of 22.6b against oracle of 19.4b and baseline of 33.8b

bsearch236.0ms

Steps

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

simplify26.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample9.2s

Algorithm

intervals

Results

3.8s	2169×	body	1280	valid
2.4s	7948×	body	80	valid
1.7s	1439×	body	640	valid
378.0ms	537×	body	320	valid
141.0ms	53×	body	2560	valid
127.0ms	248×	body	160	valid