Details

sample454.0ms

Algorithm

intervals

Results

137.0ms	255×	body	80	valid
111.0ms	55×	body	1280	valid
68.0ms	47×	body	640	valid
9.0ms	10×	body	320	valid
4.0ms	1×	body	2560	valid
4.0ms	6×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	823
4	210
3	95
2	62
1	35
0	19

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.9b	(* (atan2 x.im x.re) y.im)
1.2b	(* (atan2 x.im x.re) y.re)
29.6b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
10×	`add-cbrt-cube` `associate-r` `add-exp-log`
9×	`associate-l`
6×	`log-prod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-sum` `log-pow` `fma-udef`

Counts

4 → 81

Calls

4 calls:

14.0ms	(* y.re (log (hypot x.re x.im)))
12.0ms	(* (atan2 x.im x.re) y.im)
11.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* y.re (log (hypot x.re x.im)))
27.0ms	(* (atan2 x.im x.re) y.im)
30.0ms	(* (atan2 x.im x.re) y.re)
183.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
4	3524
3	1362
2	599
1	268
0	142

prune892.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.2b

localize77.0ms

Local error

Found 4 expressions with local error:

15.9b	(cos (* (atan2 x.im x.re) y.re))
16.1b	(sin (* (atan2 x.im x.re) y.re))
20.0b	(sin (* y.im (log (hypot x.re x.im))))
20.4b	(cos (* y.im (log (hypot x.re x.im))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `sin-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

16.0ms	(cos (* (atan2 x.im x.re) y.re))
23.0ms	(sin (* (atan2 x.im x.re) y.re))
19.0ms	(sin (* y.im (log (hypot x.re x.im))))
19.0ms	(cos (* y.im (log (hypot x.re x.im))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(cos (* (atan2 x.im x.re) y.re))
65.0ms	(sin (* (atan2 x.im x.re) y.re))
155.0ms	(sin (* y.im (log (hypot x.re x.im))))
175.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify2.6s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
4	1441
3	559
2	280
1	188
0	134

prune769.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.1b

localize139.0ms

Local error

Found 4 expressions with local error:

20.1b	(sin (* y.im (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im))))))
20.1b	(sin (* y.im (log (cbrt (hypot x.re x.im)))))
20.3b	(cos (* y.im (log (cbrt (hypot x.re x.im)))))
20.4b	(cos (* y.im (log (hypot x.re x.im))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

32×	`log-prod`
18×	`cos-sum`
16×	`distribute-rgt-in` `distribute-lft-in`
14×	`add-sqr-sqrt` `*-un-lft-identity` `sin-sum` `add-cube-cbrt`
12×	`cbrt-prod`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

24.0ms	(sin (* y.im (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im))))))
21.0ms	(sin (* y.im (log (cbrt (hypot x.re x.im)))))
14.0ms	(cos (* y.im (log (cbrt (hypot x.re x.im)))))
10.0ms	(cos (* y.im (log (hypot x.re x.im))))

series689.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(sin (* y.im (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im))))))
159.0ms	(sin (* y.im (log (cbrt (hypot x.re x.im)))))
180.0ms	(cos (* y.im (log (cbrt (hypot x.re x.im)))))
146.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify3.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
4	4294
3	1370
2	603
1	371
0	246

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.9b

localize295.0ms

Local error

Found 4 expressions with local error:

20.2b	(cos (* (log (* (cbrt (cbrt (hypot x.re x.im))) (cbrt (cbrt (hypot x.re x.im))))) y.im))
20.3b	(sin (* (log (cbrt (cbrt (hypot x.re x.im)))) y.im))
20.4b	(sin (* (log (* (cbrt (cbrt (hypot x.re x.im))) (cbrt (cbrt (hypot x.re x.im))))) y.im))
20.4b	(cos (* y.im (log (hypot x.re x.im))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `cos-sum` `log-prod` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 46

Calls

4 calls:

11.0ms	(cos (* (log (* (cbrt (cbrt (hypot x.re x.im))) (cbrt (cbrt (hypot x.re x.im))))) y.im))
9.0ms	(sin (* (log (cbrt (cbrt (hypot x.re x.im)))) y.im))
11.0ms	(sin (* (log (* (cbrt (cbrt (hypot x.re x.im))) (cbrt (cbrt (hypot x.re x.im))))) y.im))
20.0ms	(cos (* y.im (log (hypot x.re x.im))))

series936.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(cos (* (log (* (cbrt (cbrt (hypot x.re x.im))) (cbrt (cbrt (hypot x.re x.im))))) y.im))
260.0ms	(sin (* (log (cbrt (cbrt (hypot x.re x.im)))) y.im))
279.0ms	(sin (* (log (* (cbrt (cbrt (hypot x.re x.im))) (cbrt (cbrt (hypot x.re x.im))))) y.im))
141.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify2.2s

Counts

58 → 58

Iterations

Iter	Nodes
done	5002
4	2639
3	986
2	413
1	226
0	151

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.9b

regimes985.0ms

Accuracy

0% (0.7b remaining)

Error of 3.7b against oracle of 3.0b and baseline of 3.7b

bsearch0.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	63
1	63
0	47

end0.0ms

sample11.5s

Algorithm

intervals

Results

4.7s	2157×	body	1280	valid
2.8s	7975×	body	80	valid
2.2s	1384×	body	640	valid
612.0ms	230×	body	160	valid
496.0ms	555×	body	320	valid
126.0ms	42×	body	2560	valid