Details

sample373.0ms

Algorithm

intervals

Results

44.0ms	69×	body	1280	valid
25.0ms	263×	body	80	valid
22.0ms	55×	body	640	valid
5.0ms	17×	body	320	valid
2.0ms	11×	body	160	valid
1.0ms	1×	body	2560	valid

simplify674.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	19	37
1	35	26
2	63	25
3	98	25
4	215	25
5	869	25
done	5000	25

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.1b

localize22.0ms

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))
0.5b	(* (atan2 x.im x.re) y.re)
0.5b	(* (atan2 x.im x.re) y.im)
33.7b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite12.0ms

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))
3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
19.0ms	(* (atan2 x.im x.re) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
171.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.0s

Counts

72 → 72

Iterations

Useful iterations: 3 (162.0ms)

Iter	Nodes	Cost
0	101	738
1	177	728
2	409	642
3	844	638
4	1608	638
5	4832	638
done	5000	638

prune323.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.im)
0.6b	(cbrt y.im)
0.6b	(cbrt y.im)
33.7b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt y.im)
0.0ms	(cbrt y.im)
0.0ms	(cbrt y.im)
1.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt y.im)
174.0ms	(cbrt y.im)
179.0ms	(cbrt y.im)
151.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify620.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	64	433
1	105	419
2	172	377
3	322	366
4	1167	366
done	5000	366

prune357.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.im)
0.6b	(cbrt y.im)
0.6b	(cbrt y.im)
33.7b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt y.im)
1.0ms	(cbrt y.im)
1.0ms	(cbrt y.im)
1.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series698.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt y.im)
180.0ms	(cbrt y.im)
184.0ms	(cbrt y.im)
155.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify619.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	64	433
1	105	419
2	172	377
3	322	366
4	1167	366
done	5000	366

prune396.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize37.0ms

Local error

Found 4 expressions with local error:

21.2b	(cos (* (atan2 x.im x.re) y.re))
21.5b	(sin (* (atan2 x.im x.re) y.re))
22.0b	(sin (* (log (hypot x.re x.im)) y.im))
22.4b	(cos (* (log (hypot x.re x.im)) y.im))

rewrite8.0ms

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:

2.0ms	(cos (* (atan2 x.im x.re) y.re))
2.0ms	(sin (* (atan2 x.im x.re) y.re))
2.0ms	(sin (* (log (hypot x.re x.im)) y.im))
2.0ms	(cos (* (log (hypot x.re x.im)) y.im))

series335.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(cos (* (atan2 x.im x.re) y.re))
36.0ms	(sin (* (atan2 x.im x.re) y.re))
125.0ms	(sin (* (log (hypot x.re x.im)) y.im))
128.0ms	(cos (* (log (hypot x.re x.im)) y.im))

simplify2.4s

Counts

48 → 48

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	65	431
1	89	425
2	130	371
3	191	368
4	356	368
5	1036	368
done	5001	368

prune337.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

regimes309.0ms

Accuracy

91.5% (0.3b remaining)

Error of 5.8b against oracle of 5.5b and baseline of 8.6b

bsearch4.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	137
1	61	137
done	61	137

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	2157×	body	1280	valid
723.0ms	8048×	body	80	valid
559.0ms	1370×	body	640	valid
147.0ms	530×	body	320	valid
69.0ms	45×	body	2560	valid
43.0ms	231×	body	160	valid