Details

sample265.0ms

Algorithm

intervals

Results

81.0ms	247×	body	80	valid
62.0ms	62×	body	1280	valid
30.0ms	45×	body	640	valid
10.0ms	21×	body	320	valid
6.0ms	3×	body	2560	valid
2.0ms	8×	body	160	valid

simplify1.5s

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

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize50.0ms

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)))

rewrite22.0ms

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:

0.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
7.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
21.0ms	(* (atan2 x.im x.re) y.re)
35.0ms	(* (atan2 x.im x.re) y.im)
258.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.4s

Counts

72 → 72

Iterations

Useful iterations: 3 (398.0ms)

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

prune503.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize37.0ms

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))

rewrite74.0ms

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))
15.0ms	(sin (* (atan2 x.im x.re) y.re))
16.0ms	(cos (* (log (hypot x.re x.im)) y.im))
28.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series494.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cos (* (atan2 x.im x.re) y.re))
52.0ms	(sin (* (atan2 x.im x.re) y.re))
192.0ms	(cos (* (log (hypot x.re x.im)) y.im))
187.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify3.0s

Counts

48 → 48

Iterations

Useful iterations: 3 (82.0ms)

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

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))

rewrite45.0ms

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))
13.0ms	(cos (* (log (hypot x.re x.im)) y.im))
15.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series558.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cos (* (atan2 x.im x.re) y.re))
76.0ms	(sin (* (atan2 x.im x.re) y.re))
192.0ms	(cos (* (log (hypot x.re x.im)) y.im))
229.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.7s

Counts

48 → 48

Iterations

Useful iterations: 3 (58.0ms)

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

prune636.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize69.0ms

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))

rewrite56.0ms

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))
10.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series479.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(cos (* (atan2 x.im x.re) y.re))
52.0ms	(sin (* (atan2 x.im x.re) y.re))
166.0ms	(cos (* (log (hypot x.re x.im)) y.im))
178.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify3.1s

Counts

48 → 48

Iterations

Useful iterations: 3 (87.0ms)

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

prune617.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

regimes578.0ms

Accuracy

83.7% (0.5b remaining)

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

bsearch4.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.1s	2146×	body	1280	valid
2.3s	7903×	body	80	valid
1.7s	1397×	body	640	valid
451.0ms	560×	body	320	valid
137.0ms	246×	body	160	valid
98.0ms	38×	body	2560	valid