Details

sample354.0ms

Algorithm

intervals

Results

123.0ms	55×	body	1280	valid
69.0ms	255×	body	80	valid
49.0ms	47×	body	640	valid
9.0ms	10×	body	320	valid
3.0ms	1×	body	2560	valid
2.0ms	6×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.9b	(* (atan2 x.im x.re) y.im)
1.2b	(* (atan2 x.im x.re) y.re)
29.6b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite70.0ms

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×	`sin-sum` `log-pow` `fma-udef`

Counts

4 → 81

Calls

4 calls:

18.0ms	(* y.re (log (hypot x.re x.im)))
14.0ms	(* (atan2 x.im x.re) y.im)
14.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* y.re (log (hypot x.re x.im)))
18.0ms	(* (atan2 x.im x.re) y.im)
28.0ms	(* (atan2 x.im x.re) y.re)
213.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
4	3524
3	1362
2	599
1	268
0	142

prune897.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.2b

localize80.0ms

Local error

Found 4 expressions with local error:

15.9b	(cos (* (atan2 x.im x.re) y.re))
16.1b	(sin (* (atan2 x.im x.re) y.re))
20.0b	(sin (* y.im (log (hypot x.re x.im))))
20.4b	(cos (* y.im (log (hypot x.re x.im))))

rewrite91.0ms

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:

12.0ms	(cos (* (atan2 x.im x.re) y.re))
14.0ms	(sin (* (atan2 x.im x.re) y.re))
31.0ms	(sin (* y.im (log (hypot x.re x.im))))
32.0ms	(cos (* y.im (log (hypot x.re x.im))))

series425.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(cos (* (atan2 x.im x.re) y.re))
59.0ms	(sin (* (atan2 x.im x.re) y.re))
141.0ms	(sin (* y.im (log (hypot x.re x.im))))
158.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify2.2s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
4	1441
3	559
2	280
1	188
0	134

prune754.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.1b

localize180.0ms

Local error

Found 4 expressions with local error:

20.1b	(sin (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
20.1b	(sin (* (log (cbrt (hypot x.re x.im))) y.im))
20.3b	(cos (* (log (cbrt (hypot x.re x.im))) y.im))
20.4b	(cos (* y.im (log (hypot x.re x.im))))

rewrite142.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
1×	`pow2` `associate-l` `sin-2` `log-pow`

Counts

4 → 47

Calls

4 calls:

77.0ms	(sin (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
21.0ms	(sin (* (log (cbrt (hypot x.re x.im))) y.im))
15.0ms	(cos (* (log (cbrt (hypot x.re x.im))) y.im))
29.0ms	(cos (* y.im (log (hypot x.re x.im))))

series980.0ms

Counts

4 → 12

Calls

4 calls:

301.0ms	(sin (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
266.0ms	(sin (* (log (cbrt (hypot x.re x.im))) y.im))
262.0ms	(cos (* (log (cbrt (hypot x.re x.im))) y.im))
151.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify2.1s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
4	2516
3	967
2	412
1	222
0	143

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.9b

localize148.0ms

Local error

Found 4 expressions with local error:

20.0b	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
20.1b	(sin (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
20.1b	(sin (* (log (cbrt (hypot x.re x.im))) y.im))
20.4b	(cos (* y.im (log (hypot x.re x.im))))

rewrite182.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`pow2` `associate-l` `log-pow`
1×	`sin-2` `cos-2`

Counts

4 → 48

Calls

4 calls:

60.0ms	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
54.0ms	(sin (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
29.0ms	(sin (* (log (cbrt (hypot x.re x.im))) y.im))
38.0ms	(cos (* y.im (log (hypot x.re x.im))))

series900.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
256.0ms	(sin (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
242.0ms	(sin (* (log (cbrt (hypot x.re x.im))) y.im))
135.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify2.1s

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
4	2566
3	956
2	410
1	222
0	144

prune956.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.8b

regimes1.2s

Accuracy

0% (1.0b remaining)

Error of 3.9b against oracle of 3.0b and baseline of 3.9b

bsearch0.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	49
1	49
0	35

end0.0ms

sample11.7s

Algorithm

intervals

Results

5.3s	2157×	body	1280	valid
3.0s	7975×	body	80	valid
2.1s	1384×	body	640	valid
558.0ms	555×	body	320	valid
176.0ms	230×	body	160	valid
163.0ms	42×	body	2560	valid