Details

sample355.0ms

Algorithm

intervals

Results

112.0ms	59×	body	640	valid
68.0ms	59×	body	1280	valid
51.0ms	257×	body	80	valid
8.0ms	14×	body	320	valid
3.0ms	9×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

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

prune60.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize88.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
1.5b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
30.5b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite72.0ms

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:

24.0ms	(* y.re (log (hypot x.re x.im)))
15.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series739.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* y.re (log (hypot x.re x.im)))
38.0ms	(* (atan2 x.im x.re) y.re)
62.0ms	(* (atan2 x.im x.re) y.im)
434.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify4.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	1996
2	708
1	295
0	150

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.1b

localize181.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.im)
1.5b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
30.5b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `add-exp-log`
9×	`add-cbrt-cube`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
2×	`*-commutative` `unswap-sqr`
1×	`cos-sum` `pow1/3` `fma-udef`

Counts

4 → 68

Calls

4 calls:

3.0ms	(cbrt y.im)
18.0ms	(* (atan2 x.im x.re) y.re)
45.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
4.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series1.0s

Counts

4 → 12

Calls

4 calls:

331.0ms	(cbrt y.im)
64.0ms	(* (atan2 x.im x.re) y.re)
247.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
396.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify4.9s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
3	2163
2	733
1	288
0	133

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.1b

localize258.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.im)
1.5b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
30.5b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `add-exp-log`
9×	`add-cbrt-cube`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
2×	`*-commutative` `unswap-sqr`
1×	`cos-sum` `pow1/3` `fma-udef`

Counts

4 → 68

Calls

4 calls:

2.0ms	(cbrt y.im)
13.0ms	(* (atan2 x.im x.re) y.re)
61.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
8.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series985.0ms

Counts

4 → 12

Calls

4 calls:

332.0ms	(cbrt y.im)
58.0ms	(* (atan2 x.im x.re) y.re)
228.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
366.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify5.0s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
3	2163
2	733
1	288
0	133

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.1b

localize156.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
21.3b	(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
30.5b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cos-sum` `fma-udef` `remove-posit16`

Counts

4 → 64

Calls

4 calls:

10.0ms	(* (atan2 x.im x.re) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (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)))

series822.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (atan2 x.im x.re) y.re)
56.0ms	(* (atan2 x.im x.re) y.im)
382.0ms	(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
332.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify8.8s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
4	4746
3	1406
2	522
1	221
0	116

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.1b

regimes1.6s

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify15.0ms

Iterations

Iter	Nodes
done	24
1	24
0	20

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.6s	2049×	body	1280	valid
1.8s	7949×	body	80	valid
1.8s	1462×	body	640	valid
423.0ms	656×	body	320	valid
105.0ms	304×	body	160	valid