Details

sample368.0ms

Algorithm

intervals

Results

45.0ms	69×	body	1280	valid
26.0ms	263×	body	80	valid
23.0ms	55×	body	640	valid
6.0ms	17×	body	320	valid
2.0ms	11×	body	160	valid
1.0ms	1×	body	2560	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	19	37
1	35	26
2	63	25
3	98	25
4	215	25
5	859	25
done	5000	25

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.1b

localize23.0ms

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)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
17.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
174.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts

72 → 72

Iterations

Useful iterations: 3 (209.0ms)

Iter	Nodes	Cost
0	101	738
1	177	728
2	409	642
3	852	638
4	1513	638
5	3549	638
done	5001	638

prune338.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize25.0ms

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)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt y.im)
175.0ms	(cbrt y.im)
175.0ms	(cbrt y.im)
154.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.3s

Counts

61 → 61

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	64	433
1	105	419
2	172	377
3	306	366
4	641	366
5	1640	366
6	4945	366
done	5000	366

prune365.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize34.0ms

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)))

series695.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt y.im)
177.0ms	(cbrt y.im)
183.0ms	(cbrt y.im)
156.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.5s

Counts

61 → 61

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	64	433
1	105	419
2	172	377
3	306	366
4	641	366
5	1640	366
6	4945	366
done	5000	366

prune386.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize43.0ms

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))

rewrite7.0ms

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))

series329.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(cos (* (atan2 x.im x.re) y.re))
36.0ms	(sin (* (atan2 x.im x.re) y.re))
128.0ms	(sin (* (log (hypot x.re x.im)) y.im))
125.0ms	(cos (* (log (hypot x.re x.im)) y.im))

simplify2.2s

Counts

48 → 48

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	65	431
1	89	425
2	130	371
3	191	368
4	343	368
5	553	368
6	706	368
7	1048	368
8	1892	368
done	5000	368

prune342.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

regimes302.0ms

Accuracy

91.5% (0.3b remaining)

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

bsearch4.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2157×	body	1280	valid
736.0ms	8048×	body	80	valid
591.0ms	1370×	body	640	valid
156.0ms	530×	body	320	valid
69.0ms	45×	body	2560	valid
45.0ms	231×	body	160	valid