Details

sample431.0ms

Algorithm

intervals

Results

50.0ms	64×	body	1280	valid
37.0ms	257×	body	80	valid
25.0ms	43×	body	640	valid
10.0ms	27×	body	320	valid
2.0ms	10×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	19	784
1	35	654
2	62	654
3	95	654
4	210	654
5	823	654
done	5000	654

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y.re (log (hypot x.re x.im)))
1.4b	(* (atan2 x.im x.re) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
32.6b	(cos (fma (log (hypot x.re x.im)) y.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` `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 → 77

Calls

4 calls:

11.0ms	(* y.re (log (hypot x.re x.im)))
10.0ms	(* (atan2 x.im x.re) y.re)
11.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* y.re (log (hypot x.re x.im)))
20.0ms	(* (atan2 x.im x.re) y.re)
22.0ms	(* (atan2 x.im x.re) y.im)
238.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts

89 → 89

Iterations

Useful iterations: 3 (885.0ms)

Iter	Nodes	Cost
0	136	25222
1	265	24705
2	620	24583
3	1970	24238
done	5000	24238

prune879.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize65.0ms

Local error

Found 4 expressions with local error:

6.8b	(cbrt (* (atan2 x.im x.re) y.im))
6.8b	(cbrt (* (atan2 x.im x.re) y.im))
6.8b	(cbrt (* (atan2 x.im x.re) y.im))
32.6b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 43

Calls

4 calls:

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

series949.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (* (atan2 x.im x.re) y.im))
113.0ms	(cbrt (* (atan2 x.im x.re) y.im))
121.0ms	(cbrt (* (atan2 x.im x.re) y.im))
622.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts

55 → 55

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	69	20867
1	115	20863
2	185	20743
3	341	20198
4	743	19652
5	1813	18659
done	5000	18542

prune615.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize164.0ms

Local error

Found 4 expressions with local error:

6.8b	(cbrt (* (atan2 x.im x.re) y.im))
6.8b	(cbrt (* (atan2 x.im x.re) y.im))
6.8b	(cbrt (* (atan2 x.im x.re) y.im))
32.6b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 43

Calls

4 calls:

6.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (* (atan2 x.im x.re) y.im))
93.0ms	(cbrt (* (atan2 x.im x.re) y.im))
91.0ms	(cbrt (* (atan2 x.im x.re) y.im))
221.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts

55 → 55

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	69	20867
1	115	20863
2	185	20743
3	341	20198
4	743	19652
5	1813	18659
done	5000	18542

prune851.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize135.0ms

Local error

Found 4 expressions with local error:

6.8b	(cbrt (* (atan2 x.im x.re) y.im))
6.8b	(cbrt (* (atan2 x.im x.re) y.im))
6.8b	(cbrt (* (atan2 x.im x.re) y.im))
32.6b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 43

Calls

4 calls:

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

series541.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(cbrt (* (atan2 x.im x.re) y.im))
98.0ms	(cbrt (* (atan2 x.im x.re) y.im))
95.0ms	(cbrt (* (atan2 x.im x.re) y.im))
236.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.8s

Counts

55 → 55

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	69	20867
1	115	20863
2	185	20743
3	341	20198
4	743	19652
5	1813	18659
done	5000	18542

prune728.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.9b

regimes571.0ms

Accuracy

0% (0.4b remaining)

Error of 3.5b against oracle of 3.1b and baseline of 3.5b

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	23	1114
1	30	1114
done	30	1114

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.6s	2021×	body	1280	valid
2.2s	7954×	body	80	valid
1.3s	1427×	body	640	valid
443.0ms	649×	body	320	valid
131.0ms	338×	body	160	valid