Details

sample929.0ms

Algorithm

intervals

Results

624.0ms	40×	body	640	valid
156.0ms	60×	body	1280	valid
61.0ms	254×	body	80	valid
11.0ms	15×	body	320	valid
6.0ms	12×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	880
4	215
3	96
2	63
1	35
0	19

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.2b

localize53.0ms

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)))

rewrite43.0ms

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:

13.0ms	(* 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)
4.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* y.re (log (hypot x.re x.im)))
23.0ms	(* (atan2 x.im x.re) y.im)
20.0ms	(* (atan2 x.im x.re) y.re)
221.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	2489
2	805
1	296
0	150

prune813.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.2b

localize59.0ms

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))))

rewrite64.0ms

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	(sin (* (atan2 x.im x.re) y.re))
14.0ms	(cos (* (atan2 x.im x.re) y.re))
17.0ms	(sin (* y.im (log (hypot x.re x.im))))
15.0ms	(cos (* y.im (log (hypot x.re x.im))))

series418.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sin (* (atan2 x.im x.re) y.re))
43.0ms	(cos (* (atan2 x.im x.re) y.re))
167.0ms	(sin (* y.im (log (hypot x.re x.im))))
153.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify2.0s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
4	1517
3	617
2	297
1	188
0	134

prune840.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.1b

localize81.0ms

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)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(cbrt (atan2 x.im x.re))
67.0ms	(cbrt (atan2 x.im x.re))
52.0ms	(cbrt (atan2 x.im x.re))
154.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
4	2449
3	723
2	254
1	121
0	68

prune698.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

localize83.0ms

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:

2.0ms	(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)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(cbrt (atan2 x.im x.re))
69.0ms	(cbrt (atan2 x.im x.re))
73.0ms	(cbrt (atan2 x.im x.re))
162.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
4	2449
3	723
2	254
1	121
0	68

prune563.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

regimes614.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample11.3s

Algorithm

intervals

Results

4.7s	2062×	body	1280	valid
2.8s	7998×	body	80	valid
2.4s	1438×	body	640	valid
640.0ms	682×	body	320	valid
170.0ms	316×	body	160	valid