Details

sample541.0ms

Algorithm

intervals

Results

161.0ms	84×	body	1280	valid
127.0ms	261×	body	80	valid
75.0ms	49×	body	640	valid
37.0ms	3×	body	2560	valid
17.0ms	29×	body	320	valid
2.0ms	6×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	82	36
4	201	36
5	829	36
done	5000	36

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.6b

localize57.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (atan2 x.im x.re) y.im)
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite64.0ms

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:

16.0ms	(* (atan2 x.im x.re) y.im)
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
200.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.4s

Counts

68 → 68

Iterations

Useful iterations: 3 (349.0ms)

Iter	Nodes	Cost
0	98	845
1	198	787
2	442	699
3	831	686
4	1663	686
5	4083	686
done	5001	686

prune574.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.2b

localize64.0ms

Local error

Found 4 expressions with local error:

4.4b	(cbrt (atan2 x.im x.re))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(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

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

Counts

4 → 49

Calls

4 calls:

2.0ms	(cbrt (atan2 x.im x.re))
18.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(cbrt (atan2 x.im x.re))
45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
198.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.8s

Counts

61 → 61

Iterations

Useful iterations: 3 (240.0ms)

Iter	Nodes	Cost
0	85	786
1	163	727
2	325	647
3	640	631
4	1615	631
done	5000	631

prune512.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.2b

localize75.0ms

Local error

Found 4 expressions with local error:

4.4b	(cbrt (atan2 x.im x.re))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

2.0ms	(cbrt (atan2 x.im x.re))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(cbrt (atan2 x.im x.re))
59.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
233.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts

61 → 61

Iterations

Useful iterations: 3 (206.0ms)

Iter	Nodes	Cost
0	85	786
1	163	727
2	325	647
3	640	631
4	1615	631
done	5000	631

prune544.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.2b

localize74.0ms

Local error

Found 4 expressions with local error:

29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite86.0ms

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:

9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
22.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
25.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series794.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
276.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
214.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
253.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.5s

Counts

51 → 51

Iterations

Useful iterations: 3 (224.0ms)

Iter	Nodes	Cost
0	71	1005
1	144	975
2	279	851
3	547	842
4	1284	842
5	3417	842
done	5000	842

prune744.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.2b

regimes510.0ms

Accuracy

78.5% (3.1b remaining)

Error of 22.4b against oracle of 19.3b and baseline of 33.7b

bsearch347.0ms

Steps

Iters	Range		Point
10	-1.6296067729935965e-307	7.986361683910152e-295	-2.08400593192104e-310

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.2s	2078×	body	1280	valid
2.6s	7985×	body	80	valid
1.2s	1389×	body	640	valid
306.0ms	568×	body	320	valid
81.0ms	36×	body	2560	valid
72.0ms	230×	body	160	valid