Details

sample36.0ms

Algorithm

intervals

Results

15.0ms

272×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
0.5b	(fma x.re y.re (* x.im y.im))
30.9b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma y.im y.im (* y.re y.re))
0.0ms	(fma x.re y.re (* x.im y.im))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series256.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma y.im y.im (* y.re y.re))
70.0ms	(fma x.re y.re (* x.im y.im))
129.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.8s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	2677
2	461
1	116
0	73

prune443.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 30.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x.re y.re (* x.im y.im))
17.5b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
33.1b	(sqrt (fma y.im y.im (* y.re y.re)))
33.1b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 83

Calls

4 calls:

0.0ms	(fma x.re y.re (* x.im y.im))
10.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
3.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(fma x.re y.re (* x.im y.im))
158.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
86.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
81.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.3s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
3	1259
2	375
1	138
0	90

prune793.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 27.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
0.5b	(fma x.re y.re (* x.im y.im))
0.8b	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (fma x.re y.re (* x.im y.im))))
30.6b	(/ (fma y.im y.im (* y.re y.re)) (fma x.re y.re (* x.im y.im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
17×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `fma-udef`
1×	`associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma y.im y.im (* y.re y.re))
0.0ms	(fma x.re y.re (* x.im y.im))
14.0ms	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (fma x.re y.re (* x.im y.im))))
7.0ms	(/ (fma y.im y.im (* y.re y.re)) (fma x.re y.re (* x.im y.im)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(fma y.im y.im (* y.re y.re))
61.0ms	(fma x.re y.re (* x.im y.im))
218.0ms	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (fma x.re y.re (* x.im y.im))))
114.0ms	(/ (fma y.im y.im (* y.re y.re)) (fma x.re y.re (* x.im y.im)))

simplify1.4s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
2	1713
1	378
0	171

prune859.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 15.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x.im y.im (* x.re y.re))
0.0b	(/ 1 (hypot y.re y.im))
0.2b	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.im (* x.re y.re)) (hypot y.re y.im)))
17.5b	(/ (fma x.im y.im (* x.re y.re)) (hypot y.re y.im))

rewrite60.0ms

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×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 130

Calls

4 calls:

0.0ms	(fma x.im y.im (* x.re y.re))
8.0ms	(/ 1 (hypot y.re y.im))
37.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.im (* x.re y.re)) (hypot y.re y.im)))
7.0ms	(/ (fma x.im y.im (* x.re y.re)) (hypot y.re y.im))

series554.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(fma x.im y.im (* x.re y.re))
79.0ms	(/ 1 (hypot y.re y.im))
247.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.im (* x.re y.re)) (hypot y.re y.im)))
154.0ms	(/ (fma x.im y.im (* x.re y.re)) (hypot y.re y.im))

simplify2.4s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
2	3246
1	403
0	154

prune861.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.2b

regimes648.0ms

Accuracy

28.8% (8.5b remaining)

Error of 13.5b against oracle of 5.0b and baseline of 16.9b

bsearch119.0ms

Steps

Iters	Range		Point
9	1.5493309259746312e+165	3.1548477376268985e+170	7.009208612122959e+165
9	-1.791129263346789e+252	-1.6718985510668067e+245	-1.6968892796472902e+245

simplify7.0ms

Iterations

Iter	Nodes
done	32
3	32
2	29
1	26
0	20

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8471×

body

valid