Details

sample306.0ms

Algorithm

intervals

Results

89.0ms	247×	body	80	valid
71.0ms	62×	body	1280	valid
30.0ms	45×	body	640	valid
12.0ms	21×	body	320	valid
9.0ms	3×	body	2560	valid
3.0ms	8×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	19	37
1	35	26
2	63	25
3	96	25
4	215	25
5	843	25
done	5000	25

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
0.7b	(* (atan2 x.im x.re) y.re)
1.2b	(* (atan2 x.im x.re) y.im)
35.0b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`sin-sum`

Counts

4 → 60

Calls

4 calls:

1.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
14.0ms	(* (atan2 x.im x.re) y.re)
14.0ms	(* (atan2 x.im x.re) y.im)
9.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
27.0ms	(* (atan2 x.im x.re) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
250.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.2s

Counts

72 → 72

Iterations

Useful iterations: 3 (403.0ms)

Iter	Nodes	Cost
0	101	738
1	177	728
2	412	642
3	803	638
4	1496	638
5	4355	638
done	5000	638

prune464.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize77.0ms

Local error

Found 4 expressions with local error:

18.0b	(cos (* (atan2 x.im x.re) y.re))
18.3b	(sin (* (atan2 x.im x.re) y.re))
24.5b	(cos (* (log (hypot x.re x.im)) y.im))
24.8b	(sin (* (log (hypot x.re x.im)) y.im))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

11.0ms	(cos (* (atan2 x.im x.re) y.re))
8.0ms	(sin (* (atan2 x.im x.re) y.re))
8.0ms	(cos (* (log (hypot x.re x.im)) y.im))
8.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series505.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(cos (* (atan2 x.im x.re) y.re))
68.0ms	(sin (* (atan2 x.im x.re) y.re))
211.0ms	(cos (* (log (hypot x.re x.im)) y.im))
161.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.9s

Counts

48 → 48

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	65	431
1	89	425
2	128	371
3	198	368
4	305	368
5	501	368
6	656	368
7	978	368
8	2158	368
done	5001	368

prune605.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize65.0ms

Local error

Found 4 expressions with local error:

18.0b	(cos (* (atan2 x.im x.re) y.re))
18.3b	(sin (* (atan2 x.im x.re) y.re))
24.5b	(cos (* (log (hypot x.re x.im)) y.im))
24.8b	(sin (* (log (hypot x.re x.im)) y.im))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

8.0ms	(cos (* (atan2 x.im x.re) y.re))
8.0ms	(sin (* (atan2 x.im x.re) y.re))
8.0ms	(cos (* (log (hypot x.re x.im)) y.im))
9.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series570.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(cos (* (atan2 x.im x.re) y.re))
69.0ms	(sin (* (atan2 x.im x.re) y.re))
205.0ms	(cos (* (log (hypot x.re x.im)) y.im))
214.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.7s

Counts

48 → 48

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	65	431
1	89	425
2	128	371
3	198	368
4	305	368
5	501	368
6	656	368
7	978	368
8	2158	368
done	5001	368

prune565.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize77.0ms

Local error

Found 4 expressions with local error:

18.0b	(cos (* (atan2 x.im x.re) y.re))
18.3b	(sin (* (atan2 x.im x.re) y.re))
24.5b	(cos (* (log (hypot x.re x.im)) y.im))
24.8b	(sin (* (log (hypot x.re x.im)) y.im))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

16.0ms	(cos (* (atan2 x.im x.re) y.re))
15.0ms	(sin (* (atan2 x.im x.re) y.re))
15.0ms	(cos (* (log (hypot x.re x.im)) y.im))
16.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series779.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cos (* (atan2 x.im x.re) y.re))
47.0ms	(sin (* (atan2 x.im x.re) y.re))
152.0ms	(cos (* (log (hypot x.re x.im)) y.im))
534.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.8s

Counts

48 → 48

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	65	431
1	89	425
2	128	371
3	198	368
4	305	368
5	501	368
6	656	368
7	978	368
8	2158	368
done	5001	368

prune559.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

regimes573.0ms

Accuracy

83.7% (0.5b remaining)

Error of 6.4b against oracle of 5.9b and baseline of 9.2b

bsearch7.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	129
1	42	129
done	42	129

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.2s	2146×	body	1280	valid
2.5s	7903×	body	80	valid
1.5s	1397×	body	640	valid
307.0ms	560×	body	320	valid
155.0ms	246×	body	160	valid
92.0ms	38×	body	2560	valid