Details

sample445.0ms

Algorithm

intervals

Results

115.0ms	255×	body	80	valid
113.0ms	61×	body	1280	valid
31.0ms	37×	body	640	valid
11.0ms	19×	body	320	valid
9.0ms	2×	body	2560	valid
1.0ms	3×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1130
4	249
3	99
2	63
1	35
0	19

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y.re (log (hypot x.re x.im)))
0.7b	(* (atan2 x.im x.re) y.re)
2.4b	(* (atan2 x.im x.re) y.im)
34.0b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite38.0ms

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` `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 → 77

Calls

4 calls:

13.0ms	(* y.re (log (hypot x.re x.im)))
10.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* y.re (log (hypot x.re x.im)))
28.0ms	(* (atan2 x.im x.re) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)
214.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify952.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	871
1	270
0	138

prune832.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize96.0ms

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))
25.8b	(sin (* y.im (log (hypot x.re x.im))))
26.3b	(cos (* y.im (log (hypot x.re x.im))))

rewrite50.0ms

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` `log1p-expm1-u` `add-log-exp`

Counts

4 → 48

Calls

4 calls:

11.0ms	(cos (* (atan2 x.im x.re) y.re))
15.0ms	(sin (* (atan2 x.im x.re) y.re))
14.0ms	(sin (* y.im (log (hypot x.re x.im))))
8.0ms	(cos (* y.im (log (hypot x.re x.im))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(cos (* (atan2 x.im x.re) y.re))
49.0ms	(sin (* (atan2 x.im x.re) y.re))
169.0ms	(sin (* y.im (log (hypot x.re x.im))))
153.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify989.0ms

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
3	1235
2	367
1	184
0	130

prune848.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.8b

localize204.0ms

Local error

Found 4 expressions with local error:

25.9b	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
26.3b	(cos (* y.im (log (hypot x.re x.im))))
26.4b	(cos (* (log (cbrt (hypot x.re x.im))) y.im))
26.4b	(sin (* (log (cbrt (hypot x.re x.im))) y.im))

rewrite44.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 42

Calls

4 calls:

7.0ms	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
14.0ms	(cos (* y.im (log (hypot x.re x.im))))
11.0ms	(cos (* (log (cbrt (hypot x.re x.im))) y.im))
11.0ms	(sin (* (log (cbrt (hypot x.re x.im))) y.im))

series1.2s

Counts

4 → 12

Calls

4 calls:

259.0ms	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
148.0ms	(cos (* y.im (log (hypot x.re x.im))))
257.0ms	(cos (* (log (cbrt (hypot x.re x.im))) y.im))
492.0ms	(sin (* (log (cbrt (hypot x.re x.im))) y.im))

simplify1.3s

Counts

54 → 54

Iterations

Iter	Nodes
done	5001
3	1842
2	481
1	204
0	134

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.7b

localize328.0ms

Local error

Found 4 expressions with local error:

25.9b	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
26.3b	(cos (* y.im (log (hypot x.re x.im))))
26.4b	(cos (* (log (cbrt (hypot x.re x.im))) y.im))
26.4b	(sin (* (log (cbrt (hypot x.re x.im))) y.im))

rewrite53.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 42

Calls

4 calls:

13.0ms	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
15.0ms	(cos (* y.im (log (hypot x.re x.im))))
11.0ms	(cos (* (log (cbrt (hypot x.re x.im))) y.im))
11.0ms	(sin (* (log (cbrt (hypot x.re x.im))) y.im))

series1.1s

Counts

4 → 12

Calls

4 calls:

301.0ms	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
169.0ms	(cos (* y.im (log (hypot x.re x.im))))
335.0ms	(cos (* (log (cbrt (hypot x.re x.im))) y.im))
250.0ms	(sin (* (log (cbrt (hypot x.re x.im))) y.im))

simplify1.3s

Counts

54 → 54

Iterations

Iter	Nodes
done	5001
3	1842
2	481
1	204
0	134

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.7b

regimes1.2s

Accuracy

0% (0.4b remaining)

Error of 3.4b against oracle of 3.1b and baseline of 3.4b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	54
1	54
0	39

end1.0ms

sample8.8s

Algorithm

intervals

Results

3.4s	2184×	body	1280	valid
2.5s	7979×	body	80	valid
1.4s	1363×	body	640	valid
303.0ms	564×	body	320	valid
121.0ms	242×	body	160	valid
116.0ms	44×	body	2560	valid