Details

sample607.0ms

Algorithm

intervals

Results

126.0ms	59×	body	1280	valid
114.0ms	247×	body	80	valid
75.0ms	47×	body	640	valid
13.0ms	25×	body	320	valid
3.0ms	8×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (27.0ms)

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.9b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(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)
1.2b	(* (atan2 x.im x.re) y.im)
34.2b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite40.0ms

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×	`cos-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)
15.0ms	(* (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)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
33.0ms	(* (atan2 x.im x.re) y.re)
34.0ms	(* (atan2 x.im x.re) y.im)
280.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.0s

Counts

72 → 72

Iterations

Useful iterations: 3 (435.0ms)

Iter	Nodes	Cost
0	101	729
1	177	720
2	412	634
3	803	630
4	1494	630
5	4360	630
done	5000	630

prune495.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize56.0ms

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))
24.5b	(cos (* (log (hypot x.re x.im)) y.im))
24.8b	(sin (* (log (hypot x.re x.im)) y.im))

rewrite48.0ms

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:

7.0ms	(cos (* (atan2 x.im x.re) y.re))
8.0ms	(sin (* (atan2 x.im x.re) y.re))
16.0ms	(cos (* (log (hypot x.re x.im)) y.im))
16.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series571.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(cos (* (atan2 x.im x.re) y.re))
84.0ms	(sin (* (atan2 x.im x.re) y.re))
213.0ms	(cos (* (log (hypot x.re x.im)) y.im))
196.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.8s

Counts

48 → 48

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	65	431
1	89	425
2	128	371
3	198	368
4	305	368
5	501	368
6	656	368
7	978	368
8	2158	368
done	5001	368

prune559.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize62.0ms

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))
24.5b	(cos (* (log (hypot x.re x.im)) y.im))
24.8b	(sin (* (log (hypot x.re x.im)) y.im))

rewrite47.0ms

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:

9.0ms	(cos (* (atan2 x.im x.re) y.re))
15.0ms	(sin (* (atan2 x.im x.re) y.re))
8.0ms	(cos (* (log (hypot x.re x.im)) y.im))
16.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series591.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(cos (* (atan2 x.im x.re) y.re))
70.0ms	(sin (* (atan2 x.im x.re) y.re))
238.0ms	(cos (* (log (hypot x.re x.im)) y.im))
202.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify2.7s

Counts

48 → 48

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	65	431
1	89	425
2	128	371
3	198	368
4	305	368
5	501	368
6	656	368
7	978	368
8	2158	368
done	5001	368

prune634.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize102.0ms

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))
24.5b	(cos (* (log (hypot x.re x.im)) y.im))
24.8b	(sin (* (log (hypot x.re x.im)) y.im))

rewrite75.0ms

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	(cos (* (atan2 x.im x.re) y.re))
15.0ms	(sin (* (atan2 x.im x.re) y.re))
17.0ms	(cos (* (log (hypot x.re x.im)) y.im))
26.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series562.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(cos (* (atan2 x.im x.re) y.re))
75.0ms	(sin (* (atan2 x.im x.re) y.re))
199.0ms	(cos (* (log (hypot x.re x.im)) y.im))
220.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify3.1s

Counts

48 → 48

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	65	431
1	89	425
2	128	371
3	198	368
4	305	368
5	501	368
6	656	368
7	978	368
8	2158	368
done	5001	368

prune581.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

Details

sample607.0ms

simplify1.6s

prune16.0ms

localize55.0ms

rewrite40.0ms

series577.0ms

simplify5.0s

prune495.0ms

localize56.0ms

rewrite48.0ms

series571.0ms

simplify2.8s

prune559.0ms

localize62.0ms

rewrite47.0ms

series591.0ms

simplify2.7s

prune634.0ms

localize102.0ms

rewrite75.0ms

series562.0ms

simplify3.1s

prune581.0ms

regimes18.0ms