Details

sample445.0ms

Algorithm

intervals

Results

119.0ms	45×	body	640	valid
114.0ms	62×	body	1280	valid
49.0ms	247×	body	80	valid
42.0ms	21×	body	320	valid
9.0ms	3×	body	2560	valid
3.0ms	8×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (27.0ms)

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

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize53.0ms

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)))

rewrite44.0ms

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))
15.0ms	(* (atan2 x.im x.re) y.re)
15.0ms	(* (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)))

series536.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
25.0ms	(* (atan2 x.im x.re) y.re)
36.0ms	(* (atan2 x.im x.re) y.im)
282.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.6s

Counts

72 → 72

Iterations

Useful iterations: 3 (394.0ms)

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

prune625.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize74.0ms

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))

rewrite35.0ms

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))
9.0ms	(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))

series576.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(cos (* (atan2 x.im x.re) y.re))
63.0ms	(sin (* (atan2 x.im x.re) y.re))
205.0ms	(cos (* (log (hypot x.re x.im)) y.im))
225.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.9s

Counts

48 → 48

Iterations

Useful iterations: 3 (75.0ms)

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

prune585.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize88.0ms

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))

rewrite43.0ms

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))
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))

series498.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(cos (* (atan2 x.im x.re) y.re))
59.0ms	(sin (* (atan2 x.im x.re) y.re))
213.0ms	(cos (* (log (hypot x.re x.im)) y.im))
158.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.8s

Counts

48 → 48

Iterations

Useful iterations: 3 (84.0ms)

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

prune588.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize78.0ms

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))

rewrite46.0ms

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))
9.0ms	(sin (* (atan2 x.im x.re) y.re))
8.0ms	(cos (* (log (hypot x.re x.im)) y.im))
12.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series544.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(cos (* (atan2 x.im x.re) y.re))
76.0ms	(sin (* (atan2 x.im x.re) y.re))
196.0ms	(cos (* (log (hypot x.re x.im)) y.im))
225.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.9s

Counts

48 → 48

Iterations

Useful iterations: 3 (89.0ms)

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

prune593.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

regimes556.0ms

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

sample8.9s

Algorithm

intervals

Results

3.8s	2146×	body	1280	valid
2.4s	7903×	body	80	valid
1.3s	1397×	body	640	valid
363.0ms	560×	body	320	valid
96.0ms	38×	body	2560	valid
94.0ms	246×	body	160	valid