Details

sample303.0ms

Algorithm

intervals

Results

64.0ms	60×	body	1280	valid
42.0ms	254×	body	80	valid
26.0ms	40×	body	640	valid
7.0ms	15×	body	320	valid
4.0ms	12×	body	160	valid

simplify2.8s

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: 3.2b

localize79.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.6b	(* (atan2 x.im x.re) y.im)
0.9b	(* (atan2 x.im x.re) y.re)
30.9b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite48.0ms

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×	`cos-sum` `log-pow` `fma-udef`

Counts

4 → 81

Calls

4 calls:

14.0ms	(* y.re (log (hypot x.re x.im)))
11.0ms	(* (atan2 x.im x.re) y.im)
11.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* y.re (log (hypot x.re x.im)))
31.0ms	(* (atan2 x.im x.re) y.im)
29.0ms	(* (atan2 x.im x.re) y.re)
215.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
3	1949
2	719
1	296
0	150

prune827.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize71.0ms

Local error

Found 4 expressions with local error:

18.0b	(sin (* (atan2 x.im x.re) y.re))
18.1b	(cos (* (atan2 x.im x.re) y.re))
23.8b	(sin (* y.im (log (hypot x.re x.im))))
24.4b	(cos (* y.im (log (hypot x.re x.im))))

rewrite48.0ms

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:

8.0ms	(sin (* (atan2 x.im x.re) y.re))
14.0ms	(cos (* (atan2 x.im x.re) y.re))
16.0ms	(sin (* y.im (log (hypot x.re x.im))))
9.0ms	(cos (* y.im (log (hypot x.re x.im))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sin (* (atan2 x.im x.re) y.re))
74.0ms	(cos (* (atan2 x.im x.re) y.re))
145.0ms	(sin (* y.im (log (hypot x.re x.im))))
109.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify2.1s

Counts

64 → 64

Iterations

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

prune907.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize76.0ms

Local error

Found 4 expressions with local error:

3.3b	(cbrt (atan2 x.im x.re))
3.3b	(cbrt (atan2 x.im x.re))
3.3b	(cbrt (atan2 x.im x.re))
30.9b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-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×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
3.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(cbrt (atan2 x.im x.re))
54.0ms	(cbrt (atan2 x.im x.re))
75.0ms	(cbrt (atan2 x.im x.re))
206.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts

65 → 65

Iterations

Iter	Nodes
done	5019
4	2266
3	637
2	250
1	121
0	68

prune661.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize105.0ms

Local error

Found 4 expressions with local error:

3.3b	(cbrt (atan2 x.im x.re))
3.3b	(cbrt (atan2 x.im x.re))
3.3b	(cbrt (atan2 x.im x.re))
30.9b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-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×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
5.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(cbrt (atan2 x.im x.re))
63.0ms	(cbrt (atan2 x.im x.re))
53.0ms	(cbrt (atan2 x.im x.re))
164.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts

65 → 65

Iterations

Iter	Nodes
done	5019
4	2266
3	637
2	250
1	121
0	68

prune776.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

regimes834.0ms

Accuracy

0% (0.2b remaining)

Error of 3.5b against oracle of 3.3b and baseline of 3.5b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.8s	2062×	body	1280	valid
2.2s	7998×	body	80	valid
1.5s	1438×	body	640	valid
890.0ms	682×	body	320	valid
161.0ms	316×	body	160	valid