Details

sample253.0ms

Algorithm

intervals

Results

76.0ms	256×	body	80	valid
66.0ms	77×	body	1280	valid
27.0ms	47×	body	640	valid
8.0ms	22×	body	320	valid
2.0ms	7×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (22.0ms)

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize48.0ms

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

rewrite47.0ms

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:

7.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(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)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (atan2 x.im x.re) y.im)
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
227.0ms	(sin (+ (* (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 (624.0ms)

Iter	Nodes	Cost
0	98	845
1	202	787
2	554	701
3	2840	686
done	5001	686

prune746.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.6b

localize90.0ms

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

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
219.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
61.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
217.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.5s

Counts

65 → 65

Iterations

Useful iterations: 3 (192.0ms)

Iter	Nodes	Cost
0	73	1155
1	150	1073
2	308	767
3	733	718
4	2354	718
done	5001	718

prune700.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.5b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

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:

8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
202.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
205.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
232.0ms	(sin (+ (* (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 (220.0ms)

Iter	Nodes	Cost
0	71	1005
1	144	975
2	294	851
3	654	842
4	1878	842
done	5001	842

prune685.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.5b

localize51.0ms

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	(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

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:

7.0ms	(* (atan2 x.im x.re) y.im)
21.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (atan2 x.im x.re) y.im)
60.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
199.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.3s

Counts

68 → 68

Iterations

Useful iterations: 3 (579.0ms)

Iter	Nodes	Cost
0	98	845
1	202	787
2	554	701
3	2840	686
done	5001	686

prune544.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 16.5b

regimes664.0ms

Accuracy

76.6% (3.2b remaining)

Error of 22.9b against oracle of 19.7b and baseline of 33.4b

bsearch224.0ms

Steps

Iters	Range		Point
9	-2.8211790278830396e-308	4.4103299004613507e-302	-5.567353220296205e-309

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	66
1	39	66
done	39	66

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.3s	2185×	body	1280	valid
2.1s	7969×	body	80	valid
1.5s	1400×	body	640	valid
440.0ms	557×	body	320	valid
149.0ms	44×	body	2560	valid
72.0ms	209×	body	160	valid