Details

sample38.0ms

Algorithm

intervals

Results

16.0ms

270×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize19.0ms

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))
24.6b	(/ (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)))

series225.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(fma y.im y.im (* y.re y.re))
55.0ms	(fma x.re y.re (* x.im y.im))
119.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.5s

Counts

58 → 58

Iterations

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

prune431.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x.re y.re (* x.im y.im))
16.4b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.9b	(sqrt (fma y.im y.im (* y.re y.re)))
28.9b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite10.0ms

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))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(fma x.re y.re (* x.im y.im))
169.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
65.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
52.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.6s

Counts

95 → 95

Iterations

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

prune759.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.9b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x.re y.re (* x.im y.im))
24.6b	(/ (fma x.re y.re (* x.im y.im)) (* (sqrt (fma y.im y.im (* y.re y.re))) (sqrt (fma y.im y.im (* y.re y.re)))))
28.9b	(sqrt (fma y.im y.im (* y.re y.re)))
28.9b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

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))) (sqrt (fma y.im y.im (* y.re y.re)))))
6.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(fma x.re y.re (* x.im y.im))
128.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (sqrt (fma y.im y.im (* y.re y.re))) (sqrt (fma y.im y.im (* y.re y.re)))))
83.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
75.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.7s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
3	3466
2	595
1	141
0	72

prune635.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 15.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im))) (hypot y.im y.re))
0.5b	(fma y.re x.re (* x.im y.im))
0.9b	(/ 1 (* (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im))) (hypot y.im y.re)))
16.4b	(/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

27.0ms	(* (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im))) (hypot y.im y.re))
0.0ms	(fma y.re x.re (* x.im y.im))
14.0ms	(/ 1 (* (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im))) (hypot y.im y.re)))
5.0ms	(/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))

series601.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im))) (hypot y.im y.re))
52.0ms	(fma y.re x.re (* x.im y.im))
274.0ms	(/ 1 (* (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im))) (hypot y.im y.re)))
149.0ms	(/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))

simplify1.8s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	1966
1	320
0	133

prune752.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.2b

regimes534.0ms

Accuracy

0% (3.0b remaining)

Error of 16.8b against oracle of 13.8b and baseline of 16.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample1.3s

Algorithm

intervals

Results

800.0ms

8493×

body

valid