Details

sample315.0ms

Algorithm

intervals

Results

87.0ms	28×	body	640	valid
64.0ms	63×	body	1280	valid
45.0ms	250×	body	80	valid
12.0ms	18×	body	320	valid
2.0ms	6×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.5b

localize46.0ms

Local error

Found 4 expressions with local error:

3.3b	(* (atan2 x.im x.re) y.im)
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite66.0ms

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:

7.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.im)
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
249.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.8s

Counts

68 → 68

Iterations

Useful iterations: 3 (698.0ms)

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

prune608.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.2b

localize20.0ms

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))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.3b	(* (atan2 x.im x.re) y.im)
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite70.0ms

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:

10.0ms	(- (* (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)
14.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
145.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
25.0ms	(* (atan2 x.im x.re) y.im)
54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify847.0ms

Counts

78 → 78

Iterations

Useful iterations: done (845.0ms)

Iter	Nodes	Cost
0	130	1070
1	300	990
2	1018	908
done	5000	899

prune398.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.8b

localize82.0ms

Local error

Found 4 expressions with local error:

30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite123.0ms

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:

16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
40.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series726.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
215.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
209.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
230.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts

51 → 51

Iterations

Useful iterations: 3 (182.0ms)

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

prune499.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.8b

localize64.0ms

Local error

Found 4 expressions with local error:

30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite118.0ms

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:

11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
37.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
69.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
227.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
203.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

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

prune591.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.8b

regimes508.0ms

Accuracy

64.7% (5.5b remaining)

Error of 9.1b against oracle of 3.6b and baseline of 19.0b

bsearch530.0ms

Steps

Iters	Range	Point
8	-4.0720559692658706e-308	7.096957622971512e-305	-7.8827585390512e-311
10	-5.041217690362587e-243	-1.4175494366123366e-256	-1.0872065299728226e-243
8	-3.994916939001865e-91	-5.24941599863429e-95	-1.360428291412084e-94

Iters

Range

Point

-4.0720559692658706e-308

7.096957622971512e-305

-7.8827585390512e-311

-5.041217690362587e-243

-1.4175494366123366e-256

-1.0872065299728226e-243

-3.994916939001865e-91

-5.24941599863429e-95

-1.360428291412084e-94

simplify18.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	38	77
1	52	69
2	57	69
done	57	69

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.5s	2010×	body	1280	valid
2.2s	1470×	body	640	valid
2.0s	7970×	body	80	valid
483.0ms	656×	body	320	valid
101.0ms	309×	body	160	valid