Details

sample310.0ms

Algorithm

intervals

Results

121.0ms	67×	body	1280	valid
39.0ms	259×	body	80	valid
29.0ms	41×	body	640	valid
11.0ms	22×	body	320	valid
4.0ms	13×	body	160	valid
2.0ms	1×	body	2560	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	82	36
4	201	36
5	829	36
done	5000	36

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize50.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) y.im)
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `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 → 56

Calls

4 calls:

11.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (atan2 x.im x.re) y.im)
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
269.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.1s

Counts

68 → 68

Iterations

Useful iterations: 3 (373.0ms)

Iter	Nodes	Cost
0	98	845
1	198	787
2	442	699
3	831	686
4	1663	686
5	4083	686
done	5001	686

prune560.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.6b

localize61.0ms

Local error

Found 4 expressions with local error:

30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.7b	(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` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sin-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 39

Calls

4 calls:

8.0ms	(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)))
18.0ms	(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)))

series704.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
216.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
186.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
257.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.5s

Counts

51 → 51

Iterations

Useful iterations: 3 (185.0ms)

Iter	Nodes	Cost
0	71	1005
1	144	975
2	279	851
3	547	842
4	1284	842
5	3417	842
done	5000	842

prune589.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 19.6b

localize47.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) y.im)
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `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 → 56

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.im)
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (atan2 x.im x.re) y.im)
48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
240.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.0s

Counts

68 → 68

Iterations

Useful iterations: 3 (365.0ms)

Iter	Nodes	Cost
0	98	845
1	198	787
2	442	699
3	831	686
4	1663	686
5	4083	686
done	5001	686

prune561.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 19.6b

localize58.0ms

Local error

Found 4 expressions with local error:

30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
34.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sin-sum`

Counts

4 → 49

Calls

4 calls:

9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
150.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
173.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
246.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts

61 → 61

Iterations

Useful iterations: 3 (720.0ms)

Iter	Nodes	Cost
0	96	941
1	195	901
2	385	779
3	774	772
4	1942	772
done	5000	772

prune625.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 19.6b

regimes623.0ms

Accuracy

79.1% (3.0b remaining)

Error of 22.4b against oracle of 19.3b and baseline of 33.8b

bsearch231.0ms

Steps

Iters	Range		Point
10	-1.9739641733344554e-305	8.845804037490812e-301	-5.774698178669197e-309

simplify33.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	66
1	39	66
done	39	66

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.2s	2175×	body	1280	valid
2.0s	1425×	body	640	valid
1.7s	7945×	body	80	valid
767.0ms	576×	body	320	valid
167.0ms	50×	body	2560	valid
78.0ms	249×	body	160	valid