Details

sample288.0ms

Algorithm

intervals

Results

76.0ms	247×	body	80	valid
43.0ms	59×	body	1280	valid
25.0ms	47×	body	640	valid
11.0ms	25×	body	320	valid
2.0ms	8×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.9b

localize48.0ms

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)))

rewrite41.0ms

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))
14.0ms	(* (atan2 x.im x.re) y.re)
13.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series574.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
23.0ms	(* (atan2 x.im x.re) y.re)
23.0ms	(* (atan2 x.im x.re) y.im)
300.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.1s

Counts

72 → 72

Iterations

Useful iterations: 3 (341.0ms)

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

prune575.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize90.0ms

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))

rewrite62.0ms

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:

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

series528.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(cos (* (atan2 x.im x.re) y.re))
77.0ms	(sin (* (atan2 x.im x.re) y.re))
204.0ms	(cos (* (log (hypot x.re x.im)) y.im))
201.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.8s

Counts

48 → 48

Iterations

Useful iterations: 3 (83.0ms)

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

prune644.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize95.0ms

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))

rewrite57.0ms

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))
25.0ms	(cos (* (log (hypot x.re x.im)) y.im))
16.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series587.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(cos (* (atan2 x.im x.re) y.re))
72.0ms	(sin (* (atan2 x.im x.re) y.re))
229.0ms	(cos (* (log (hypot x.re x.im)) y.im))
208.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify3.3s

Counts

48 → 48

Iterations

Useful iterations: 3 (106.0ms)

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

prune542.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize82.0ms

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))

rewrite53.0ms

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))
21.0ms	(cos (* (log (hypot x.re x.im)) y.im))
15.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series513.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(cos (* (atan2 x.im x.re) y.re))
58.0ms	(sin (* (atan2 x.im x.re) y.re))
190.0ms	(cos (* (log (hypot x.re x.im)) y.im))
213.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.8s

Counts

48 → 48

Iterations

Useful iterations: 3 (79.0ms)

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

prune583.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

regimes437.0ms

Accuracy

82.9% (0.5b remaining)

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

bsearch4.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	143
1	56	143
done	56	143

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.9s	1963×	body	1280	valid
1.8s	7927×	body	80	valid
1.6s	1424×	body	640	valid
845.0ms	654×	body	320	valid
112.0ms	322×	body	160	valid