Details

sample879.0ms

Algorithm

intervals

Results

667.0ms	45×	body	640	valid
71.0ms	69×	body	1280	valid
41.0ms	257×	body	80	valid
9.0ms	19×	body	320	valid
4.0ms	14×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1115
4	236
3	85
2	53
1	31
0	19

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize104.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.im)
26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
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:

10.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (atan2 x.im x.re) y.im)
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
235.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
3	2779
2	562
1	199
0	96

prune614.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(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)
1.2b	(* (atan2 x.im x.re) y.im)
26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

15.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
9.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
9.0ms	(* (atan2 x.im x.re) y.im)
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
133.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
31.0ms	(* (atan2 x.im x.re) y.im)
58.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.2s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	953
1	293
0	133

prune680.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.0b

localize110.0ms

Local error

Found 4 expressions with local error:

3.3b	(cbrt (atan2 x.im x.re))
26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(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)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(cbrt (atan2 x.im x.re))
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
198.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts

61 → 61

Iterations

Iter	Nodes
done	5002
4	2626
3	851
2	356
1	161
0	82

prune717.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.0b

localize187.0ms

Local error

Found 4 expressions with local error:

26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.4b	(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

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `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)))
17.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
24.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
14.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series716.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
223.0ms	(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)))
233.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
4	1878
3	652
2	289
1	139
0	68

prune741.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.0b

regimes837.0ms

Accuracy

80.1% (5.8b remaining)

Error of 9.3b against oracle of 3.5b and baseline of 32.7b

bsearch403.0ms

Steps

Iters	Range		Point
10	-8.38583807968836e-299	6.218782843424262e-302	-4.3999011435792e-310
2	-5.403457229871107e-30	-4.784620847803006e-30	-5.3261026821125945e-30
7	-78527178.93455619	-2719823.3768185643	-2759744.904025152

simplify12.0ms

Iterations

Iter	Nodes
done	51
2	51
1	48
0	38

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.1s	7984×	body	80	valid
2.8s	2050×	body	1280	valid
1.4s	1496×	body	640	valid
396.0ms	660×	body	320	valid
106.0ms	295×	body	160	valid