Details

sample592.0ms

Algorithm

intervals

Results

153.0ms	71×	body	1280	valid
56.0ms	258×	body	80	valid
47.0ms	47×	body	640	valid
18.0ms	26×	body	320	valid
3.0ms	7×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.3b

localize66.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (atan2 x.im x.re) y.im)
26.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite75.0ms

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×	`cos-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)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms	(cos (+ (* (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:

32.0ms	(* (atan2 x.im x.re) y.im)
70.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
60.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
214.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts

68 → 68

Iterations

Useful iterations: 3 (619.0ms)

Iter	Nodes	Cost
0	95	836
1	197	778
2	554	692
3	2818	677
done	5000	677

prune674.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.6b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.1b	(* (atan2 x.im x.re) y.im)
26.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r`
3×	`exp-prod` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 69

Calls

4 calls:

33.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
26.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
8.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
143.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
33.0ms	(* (atan2 x.im x.re) y.im)
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify762.0ms

Counts

81 → 81

Iterations

Useful iterations: done (759.0ms)

Iter	Nodes	Cost
0	132	1042
1	290	985
2	920	871
done	5000	867

prune672.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.3b

localize95.0ms

Local error

Found 4 expressions with local error:

26.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite101.0ms

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×	`cos-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)))
35.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
20.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
28.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
185.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
197.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
213.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts

51 → 51

Iterations

Useful iterations: 3 (165.0ms)

Iter	Nodes	Cost
0	68	978
1	139	948
2	289	824
3	651	815
4	1869	815
done	5001	815

prune731.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.3b

localize68.0ms

Local error

Found 4 expressions with local error:

26.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
20.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
237.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
251.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts

58 → 58

Iterations

Useful iterations: 3 (213.0ms)

Iter	Nodes	Cost
0	68	936
1	139	880
2	289	776
3	651	762
4	1869	762
done	5001	762

prune681.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.3b

regimes581.0ms

Accuracy

68.2% (5.3b remaining)

Error of 8.7b against oracle of 3.5b and baseline of 20.0b

bsearch158.0ms

Steps

Iters	Range		Point
9	-2.8211790278830396e-308	4.4103299004613507e-302	4.71163328646245e-310

simplify11.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	33
1	34	29
2	38	29
done	38	29

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.4s	1993×	body	1280	valid
1.8s	8004×	body	80	valid
1.7s	1432×	body	640	valid
338.0ms	655×	body	320	valid
96.0ms	280×	body	160	valid