Details

sample475.0ms

Algorithm

intervals

Results

134.0ms	256×	body	80	valid
117.0ms	80×	body	1280	valid
43.0ms	47×	body	640	valid
10.0ms	17×	body	320	valid
8.0ms	3×	body	2560	valid
6.0ms	14×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	85	36
4	220	36
5	1023	36
done	5000	36

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.1b

localize69.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite70.0ms

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:

15.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sqrt (+ (* 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)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (atan2 x.im x.re) y.im)
59.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
69.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
291.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.2s

Counts

68 → 68

Iterations

Useful iterations: 3 (681.0ms)

Iter	Nodes	Cost
0	98	845
1	202	787
2	554	701
3	2840	686
done	5001	686

prune600.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.2b

localize44.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite113.0ms

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:

17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(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)))
38.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series697.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
208.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
224.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
221.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

51 → 51

Iterations

Useful iterations: 3 (197.0ms)

Iter	Nodes	Cost
0	71	1005
1	144	975
2	294	851
3	654	842
4	1878	842
done	5001	842

prune685.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.2b

localize86.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.3b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite284.0ms

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:

17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
19.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
213.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series759.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(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)))
222.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
248.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts

51 → 51

Iterations

Useful iterations: 3 (233.0ms)

Iter	Nodes	Cost
0	87	1257
1	169	1227
2	328	881
3	775	842
4	2453	842
done	5002	842

prune639.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.2b

localize88.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.3b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite471.0ms

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:

13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
37.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
400.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

series715.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
213.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
207.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
249.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts

51 → 51

Iterations

Useful iterations: 3 (156.0ms)

Iter	Nodes	Cost
0	89	1509
1	174	1479
2	338	1091
3	827	842
4	3133	842
done	5001	842

prune656.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.2b

regimes434.0ms

Accuracy

78.8% (3.0b remaining)

Error of 22.2b against oracle of 19.2b and baseline of 33.4b

bsearch290.0ms

Steps

Iters	Range		Point
11	-2.8777477469784756e-294	1.4337929867489595e-303	-2.19425972553957e-310

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	65
1	39	65
done	39	65

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.1s	2205×	body	1280	valid
2.3s	7937×	body	80	valid
2.0s	1409×	body	640	valid
320.0ms	584×	body	320	valid
110.0ms	44×	body	2560	valid
85.0ms	254×	body	160	valid