Details

sample21.0ms

Algorithm

intervals

Results

8.0ms

266×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	11	15
1	17	13
2	21	13
done	21	13

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma x.re y.re (* x.im y.im))
28.4b	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma x.re y.re (* x.im y.im))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

series136.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(fma x.re y.re (* x.im y.im))
96.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

simplify1.8s

Counts

45 → 45

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	65	725
1	101	714
2	250	622
3	726	622
4	2199	622
done	5001	622

prune141.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma y.re x.re (* y.im x.im))
0.0b	(/ 1 (hypot y.re y.im))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
16.6b	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 130

Calls

4 calls:

0.0ms	(fma y.re x.re (* y.im x.im))
5.0ms	(/ 1 (hypot y.re y.im))
22.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
5.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

series387.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma y.re x.re (* y.im x.im))
51.0ms	(/ 1 (hypot y.re y.im))
184.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
108.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

simplify2.8s

Counts

142 → 142

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	152	2192
1	349	2009
2	1100	1759
3	3957	1759
done	5000	1726

prune336.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.re x.re (* y.im x.im))
0.1b	(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
16.6b	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`fma-udef` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

0.0ms	(fma y.re x.re (* y.im x.im))
10.0ms	(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
5.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

series276.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(fma y.re x.re (* y.im x.im))
125.0ms	(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
111.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

simplify1.4s

Counts

120 → 120

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	159	2484
1	320	2423
2	705	2246
3	2029	2192
done	5000	2130

prune326.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma y.re x.re (* y.im x.im))
0.1b	(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))) (hypot y.re y.im))
0.2b	(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im))))
16.6b	(/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
50×	`associate-/l*`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 319

Calls

4 calls:

0.0ms	(fma y.re x.re (* y.im x.im))
22.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))) (hypot y.re y.im))
9.0ms	(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im))))
5.0ms	(/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma y.re x.re (* y.im x.im))
181.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))) (hypot y.re y.im))
118.0ms	(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im))))
99.0ms	(/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))

simplify1.3s

Counts

331 → 331

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	457	8797
1	1011	7708
2	1898	7150
done	5000	6968

prune560.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.4b

regimes168.0ms

Accuracy

34.8% (7.3b remaining)

Error of 13.2b against oracle of 6.0b and baseline of 17.1b

bsearch72.0ms

Steps

Iters	Range		Point
8	2.5290916539296384e+176	1.2288273184511015e+181	1.743552084367146e+178
9	-1.0864288282932928e+169	-4.354416350763856e+162	-4.57826742033894e+162

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	22	39
1	29	33
2	32	33
done	32	33

end0.0ms

sample554.0ms

Algorithm

intervals

Results

271.0ms

8444×

body

valid