Details

sample30.0ms

Algorithm

intervals

Results

16.0ms

271×

body

valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize25.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma x.re y.re (* x.im y.im))
24.1b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

2 → 41

Calls

2 calls:

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

series194.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(fma x.re y.re (* x.im y.im))
134.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify2.7s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
4	3356
3	936
2	296
1	106
0	67

prune252.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma x.re y.re (* x.im y.im))
15.7b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite11.0ms

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` `insert-posit16` `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 → 87

Calls

4 calls:

0.0ms	(fma x.re y.re (* x.im y.im))
7.0ms	(/ (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)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(fma x.re y.re (* x.im y.im))
134.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
64.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
66.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.0s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
4	2629
3	857
2	304
1	143
0	93

prune535.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma x.re y.re (* x.im y.im))
15.8b	(* (fma x.re y.re (* x.im y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`-un-lft-identity` `times-frac` `associate-r*`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `fma-udef`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `cbrt-unprod` `hypot-def`
1×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

0.0ms	(fma x.re y.re (* x.im y.im))
16.0ms	(* (fma x.re y.re (* x.im y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma x.re y.re (* x.im y.im))
134.0ms	(* (fma x.re y.re (* x.im y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
57.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
69.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.6s

Counts

107 → 107

Iterations

Iter	Nodes
done	5008
3	1875
2	600
1	246
0	116

prune574.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.2b

localize52.0ms

Local error

Found 4 expressions with local error:

8.3b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
9×	`associate-/r*`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef` `hypot-def` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 105

Calls

4 calls:

5.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
74.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
74.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
62.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.1s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
4	2077
3	786
2	344
1	188
0	120

prune873.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.2b

regimes373.0ms

Accuracy

0% (2.4b remaining)

Error of 25.8b against oracle of 23.3b and baseline of 25.8b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample916.0ms

Algorithm

intervals

Results

664.0ms

8459×

body

valid