Details

sample322.0ms

Algorithm

intervals

Results

79.0ms	40×	body	640	valid
61.0ms	54×	body	1280	valid
39.0ms	255×	body	80	valid
7.0ms	14×	body	320	valid
3.0ms	8×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	19	37
1	35	26
2	63	25
3	96	25
4	215	25
5	843	25
done	5000	25

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
0.7b	(* (atan2 x.im x.re) y.re)
0.9b	(* (atan2 x.im x.re) y.im)
31.9b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`sin-sum`

Counts

4 → 60

Calls

4 calls:

1.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
14.0ms	(* (atan2 x.im x.re) y.re)
14.0ms	(* (atan2 x.im x.re) y.im)
9.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series571.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
35.0ms	(* (atan2 x.im x.re) y.re)
35.0ms	(* (atan2 x.im x.re) y.im)
290.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.1s

Counts

72 → 72

Iterations

Useful iterations: 3 (355.0ms)

Iter	Nodes	Cost
0	101	738
1	177	728
2	412	642
3	803	638
4	1496	638
5	4355	638
done	5000	638

prune527.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize31.0ms

Local error

Found 4 expressions with local error:

3.7b	(cbrt (atan2 x.im x.re))
3.7b	(cbrt (atan2 x.im x.re))
3.7b	(cbrt (atan2 x.im x.re))
31.9b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
7.0ms	(cbrt (atan2 x.im x.re))
3.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(cbrt (atan2 x.im x.re))
80.0ms	(cbrt (atan2 x.im x.re))
63.0ms	(cbrt (atan2 x.im x.re))
226.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts

61 → 61

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	57	538
1	88	524
2	143	464
3	237	453
4	559	453
5	2156	453
done	5000	453

prune472.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize51.0ms

Local error

Found 4 expressions with local error:

3.7b	(cbrt (atan2 x.im x.re))
3.7b	(cbrt (atan2 x.im x.re))
3.7b	(cbrt (atan2 x.im x.re))
31.9b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

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	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cbrt (atan2 x.im x.re))
53.0ms	(cbrt (atan2 x.im x.re))
71.0ms	(cbrt (atan2 x.im x.re))
239.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts

61 → 61

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	57	538
1	88	524
2	143	464
3	237	453
4	559	453
5	2156	453
done	5000	453

prune595.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize113.0ms

Local error

Found 4 expressions with local error:

19.9b	(sin (* (atan2 x.im x.re) y.re))
20.2b	(cos (* (atan2 x.im x.re) y.re))
22.2b	(sin (* (log (hypot x.re x.im)) y.im))
22.2b	(cos (* (log (hypot x.re x.im)) y.im))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

15.0ms	(sin (* (atan2 x.im x.re) y.re))
15.0ms	(cos (* (atan2 x.im x.re) y.re))
29.0ms	(sin (* (log (hypot x.re x.im)) y.im))
15.0ms	(cos (* (log (hypot x.re x.im)) y.im))

series605.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sin (* (atan2 x.im x.re) y.re))
78.0ms	(cos (* (atan2 x.im x.re) y.re))
239.0ms	(sin (* (log (hypot x.re x.im)) y.im))
211.0ms	(cos (* (log (hypot x.re x.im)) y.im))

simplify3.2s

Counts

48 → 48

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	65	431
1	89	425
2	128	371
3	198	368
4	305	368
5	501	368
6	652	368
7	978	368
8	2135	368
done	5000	368

prune534.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

regimes571.0ms

Accuracy

85.7% (0.4b remaining)

Error of 6.2b against oracle of 5.8b and baseline of 8.8b

bsearch4.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	132
1	56	132
done	56	132

end0.0ms

sample8.5s

Algorithm

intervals

Results

2.8s	2113×	body	1280	valid
2.2s	7966×	body	80	valid
2.0s	1370×	body	640	valid
361.0ms	587×	body	320	valid
141.0ms	30×	body	2560	valid
84.0ms	237×	body	160	valid