Details

sample354.0ms

Algorithm

intervals

Results

38.0ms	65×	body	1280	valid
21.0ms	255×	body	80	valid
20.0ms	53×	body	640	valid
8.0ms	22×	body	320	valid
2.0ms	9×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	84	36
4	201	36
5	841	36
done	5000	36

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.8b

localize31.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
26.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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:

3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
155.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

68 → 68

Iterations

Useful iterations: 3 (177.0ms)

Iter	Nodes	Cost
0	95	836
1	193	778
2	438	690
3	876	677
4	1624	677
5	3675	677
done	5000	677

prune323.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 17.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (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)
1.7b	(* (atan2 x.im x.re) y.im)
26.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

3.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
90.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.5s

Counts

78 → 78

Iterations

Useful iterations: 3 (428.0ms)

Iter	Nodes	Cost
0	130	1070
1	292	990
2	770	908
3	2004	892
4	4711	892
done	5000	892

prune268.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.9b

localize29.0ms

Local error

Found 4 expressions with local error:

26.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

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:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
135.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
132.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
133.0ms	(cos (+ (* (log (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 (92.0ms)

Iter	Nodes	Cost
0	68	978
1	139	948
2	273	824
3	555	815
4	1187	815
5	2898	815
done	5000	815

prune329.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.8b

localize32.0ms

Local error

Found 4 expressions with local error:

26.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
136.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
141.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts

58 → 58

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	68	936
1	139	880
2	273	776
3	555	762
4	1187	762
5	2898	762
done	5000	762

prune372.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.8b

regimes224.0ms

Accuracy

64.8% (5.8b remaining)

Error of 9.3b against oracle of 3.5b and baseline of 19.9b

bsearch374.0ms

Steps

Iters	Range		Point
10	5.082857295074302e-16	0.44834868164545755	0.003585487534111657
8	1.5558108058645858e-183	3.4979177549211033e-180	2.3631313779480035e-180
7	1.3072171238528887e-291	1.7607007941601373e-289	1.551279700320499e-291
7	-3.907209022983326e-220	-8.922429079776871e-222	-2.9876182964047036e-221

simplify9.0ms

Iterations

Useful iterations: done (9.0ms)

Iter	Nodes	Cost
0	41	98
1	58	78
2	63	61
3	66	61
done	66	60

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	2028×	body	1280	valid
670.0ms	8025×	body	80	valid
601.0ms	1534×	body	640	valid
200.0ms	690×	body	320	valid
53.0ms	305×	body	160	valid