Details

sample266.0ms

Algorithm

intervals

Results

77.0ms	53×	body	640	valid
47.0ms	256×	body	80	valid
46.0ms	43×	body	1280	valid
9.0ms	16×	body	320	valid
3.0ms	6×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.1b

localize41.0ms

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)
29.7b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

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:

12.0ms	(* y.re (log (hypot x.re x.im)))
7.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(* (atan2 x.im x.re) y.re)
5.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* y.re (log (hypot x.re x.im)))
18.0ms	(* (atan2 x.im x.re) y.im)
25.0ms	(* (atan2 x.im x.re) y.re)
217.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
3	1949
2	719
1	296
0	150

prune888.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.re)
0.9b	(* (atan2 x.im x.re) y.im)
1.3b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
30.0b	(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
36×	`associate-r`
25×	`cbrt-prod`
18×	`unswap-sqr`
17×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube`
12×	`associate-l`
11×	`pow1` `add-exp-log`
10×	`cbrt-unprod`
8×	`swap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cos-sum` `pow1/3` `fma-udef`

Counts

4 → 105

Calls

4 calls:

1.0ms	(cbrt y.re)
15.0ms	(* (atan2 x.im x.re) y.im)
96.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
6.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series660.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(cbrt y.re)
30.0ms	(* (atan2 x.im x.re) y.im)
115.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
204.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify2.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
3	3592
2	1233
1	442
0	184

prune791.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.1b

localize90.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt y.re) (cbrt y.re)))
0.9b	(* (atan2 x.im x.re) y.im)
1.0b	(* (atan2 x.im x.re) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (* (cbrt y.re) (cbrt y.re)))))
29.9b	(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (atan2 x.im x.re) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (* (cbrt y.re) (cbrt y.re))))) (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt y.re))))

rewrite552.0ms

Algorithm

rewrite-expression-head

Rules

889×	`cbrt-prod`
839×	`add-sqr-sqrt`
516×	`unswap-sqr`
266×	`associate-r`
176×	`swap-sqr`
68×	`associate-l`
61×	`*-un-lft-identity`
57×	`add-cube-cbrt`
55×	`*-commutative`
16×	`add-cbrt-cube`
11×	`pow1` `add-exp-log`
10×	`cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cos-sum` `pow1/3` `fma-udef`

Counts

4 → 415

Calls

4 calls:

10.0ms	(cbrt (* (cbrt y.re) (cbrt y.re)))
7.0ms	(* (atan2 x.im x.re) y.im)
485.0ms	(* (atan2 x.im x.re) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (* (cbrt y.re) (cbrt y.re)))))
5.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (atan2 x.im x.re) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (* (cbrt y.re) (cbrt y.re))))) (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt y.re))))

series947.0ms

Counts

4 → 12

Calls

4 calls:

414.0ms	(cbrt (* (cbrt y.re) (cbrt y.re)))
30.0ms	(* (atan2 x.im x.re) y.im)
265.0ms	(* (atan2 x.im x.re) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (* (cbrt y.re) (cbrt y.re)))))
238.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (atan2 x.im x.re) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (* (cbrt y.re) (cbrt y.re))))) (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt y.re))))

simplify2.4s

Counts

427 → 427

Iterations

Iter	Nodes
done	5001
2	2182
1	1101
0	450

prune2.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.1b

localize114.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt y.re) (cbrt y.re)))
0.7b	(* (atan2 x.im x.re) (* (cbrt (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt (cbrt (* (cbrt y.re) (cbrt y.re))))))
0.9b	(* (atan2 x.im x.re) y.im)
29.7b	(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (* (atan2 x.im x.re) (* (cbrt (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt (cbrt (* (cbrt y.re) (cbrt y.re)))))) (* (cbrt (* (cbrt (cbrt y.re)) (cbrt y.re))) (cbrt (* (cbrt (cbrt y.re)) (cbrt y.re))))) (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt y.re))))

rewrite592.0ms

Algorithm

rewrite-expression-head

Rules

1557×	`cbrt-prod`
967×	`add-sqr-sqrt`
596×	`unswap-sqr`
299×	`associate-r`
188×	`swap-sqr`
71×	`associate-l`
65×	`*-un-lft-identity`
61×	`add-cube-cbrt`
59×	`*-commutative`
16×	`add-cbrt-cube`
11×	`pow1` `add-exp-log`
10×	`cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cos-sum` `pow1/3` `fma-udef`

Counts

4 → 467

Calls

4 calls:

14.0ms	(cbrt (* (cbrt y.re) (cbrt y.re)))
504.0ms	(* (atan2 x.im x.re) (* (cbrt (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt (cbrt (* (cbrt y.re) (cbrt y.re))))))
7.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (* (atan2 x.im x.re) (* (cbrt (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt (cbrt (* (cbrt y.re) (cbrt y.re)))))) (* (cbrt (* (cbrt (cbrt y.re)) (cbrt y.re))) (cbrt (* (cbrt (cbrt y.re)) (cbrt y.re))))) (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt y.re))))

series1.3s

Counts

4 → 12

Calls

4 calls:

867.0ms	(cbrt (* (cbrt y.re) (cbrt y.re)))
248.0ms	(* (atan2 x.im x.re) (* (cbrt (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt (cbrt (* (cbrt y.re) (cbrt y.re))))))
18.0ms	(* (atan2 x.im x.re) y.im)
199.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (* (atan2 x.im x.re) (* (cbrt (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt (cbrt (* (cbrt y.re) (cbrt y.re)))))) (* (cbrt (* (cbrt (cbrt y.re)) (cbrt y.re))) (cbrt (* (cbrt (cbrt y.re)) (cbrt y.re))))) (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt y.re))))

simplify2.9s

Counts

479 → 479

Iterations

Iter	Nodes
done	5000
2	2503
1	1304
0	537

prune3.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.1b

regimes319.0ms

Accuracy

0% (0.0b remaining)

Error of 3.2b against oracle of 3.2b and baseline of 3.2b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample10.8s

Algorithm

intervals

Results

4.0s	1961×	body	1280	valid
2.8s	1444×	body	640	valid
2.7s	8009×	body	80	valid
575.0ms	638×	body	320	valid
156.0ms	291×	body	160	valid