Details

sample286.0ms

Algorithm

intervals

Results

75.0ms	47×	body	640	valid
58.0ms	59×	body	1280	valid
42.0ms	247×	body	80	valid
12.0ms	25×	body	320	valid
2.0ms	8×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (28.0ms)

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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.9b

localize24.0ms

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)
34.2b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

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×	`cos-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))
9.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(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)
33.0ms	(* (atan2 x.im x.re) y.im)
278.0ms	(cos (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 (407.0ms)

Iter	Nodes	Cost
0	101	729
1	177	720
2	412	634
3	803	630
4	1494	630
5	4360	630
done	5000	630

prune459.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize72.0ms

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))

rewrite34.0ms

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:

7.0ms	(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))
11.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series532.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(cos (* (atan2 x.im x.re) y.re))
79.0ms	(sin (* (atan2 x.im x.re) y.re))
188.0ms	(cos (* (log (hypot x.re x.im)) y.im))
199.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.8s

Counts

48 → 48

Iterations

Useful iterations: 3 (76.0ms)

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

prune571.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize73.0ms

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))

rewrite75.0ms

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:

27.0ms	(cos (* (atan2 x.im x.re) y.re))
15.0ms	(sin (* (atan2 x.im x.re) y.re))
16.0ms	(cos (* (log (hypot x.re x.im)) y.im))
15.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series481.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cos (* (atan2 x.im x.re) y.re))
62.0ms	(sin (* (atan2 x.im x.re) y.re))
190.0ms	(cos (* (log (hypot x.re x.im)) y.im))
175.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.8s

Counts

48 → 48

Iterations

Useful iterations: 3 (55.0ms)

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

prune687.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize59.0ms

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))

rewrite48.0ms

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:

14.0ms	(cos (* (atan2 x.im x.re) y.re))
14.0ms	(sin (* (atan2 x.im x.re) y.re))
10.0ms	(cos (* (log (hypot x.re x.im)) y.im))
8.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series562.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(cos (* (atan2 x.im x.re) y.re))
59.0ms	(sin (* (atan2 x.im x.re) y.re))
208.0ms	(cos (* (log (hypot x.re x.im)) y.im))
225.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify3.3s

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

prune536.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

regimes544.0ms

Accuracy

82.9% (0.5b remaining)

Error of 6.1b against oracle of 5.6b and baseline of 8.6b

bsearch7.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	42	141
1	54	141
done	54	141

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.6s	1963×	body	1280	valid
2.3s	7927×	body	80	valid
1.6s	1424×	body	640	valid
463.0ms	654×	body	320	valid
113.0ms	322×	body	160	valid