Details

sample308.0ms

Algorithm

intervals

Results

96.0ms	59×	body	1280	valid
46.0ms	59×	body	640	valid
45.0ms	257×	body	80	valid
8.0ms	14×	body	320	valid
3.0ms	9×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

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

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize38.0ms

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)))

rewrite50.0ms

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:

27.0ms	(* y.re (log (hypot x.re x.im)))
7.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* y.re (log (hypot x.re x.im)))
30.0ms	(* (atan2 x.im x.re) y.re)
32.0ms	(* (atan2 x.im x.re) y.im)
190.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
3	2037
2	736
1	298
0	150

prune861.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.1b

localize67.0ms

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)))

rewrite48.0ms

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:

1.0ms	(cbrt y.im)
14.0ms	(* (atan2 x.im x.re) y.re)
27.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
3.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series581.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(cbrt y.im)
19.0ms	(* (atan2 x.im x.re) y.re)
118.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
179.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	2124
2	735
1	287
0	133

prune704.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.0b

localize72.0ms

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)))

rewrite38.0ms

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:

1.0ms	(cbrt y.im)
9.0ms	(* (atan2 x.im x.re) y.re)
22.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
3.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series574.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(cbrt y.im)
30.0ms	(* (atan2 x.im x.re) y.re)
123.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
151.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	2124
2	735
1	287
0	133

prune868.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.0b

localize108.0ms

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)))

rewrite35.0ms

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:

14.0ms	(* (atan2 x.im x.re) y.re)
14.0ms	(* (atan2 x.im x.re) y.im)
0.0ms	(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (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)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.re)
18.0ms	(* (atan2 x.im x.re) y.im)
136.0ms	(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
199.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
3	1445
2	495
1	219
0	116

prune902.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.0b

regimes477.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	24
1	24
0	20

end0.0ms

sample7.9s

Algorithm

intervals

Results

3.6s	2049×	body	1280	valid
1.8s	7949×	body	80	valid
1.5s	1462×	body	640	valid
425.0ms	656×	body	320	valid
108.0ms	304×	body	160	valid