Details

sample35.0ms

Algorithm

intervals

Results

19.0ms

273×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
1.3b	(fma x.re y.re (* x.im y.im))
25.6b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite7.0ms

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

series236.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(fma y.im y.im (* y.re y.re))
59.0ms	(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)))

simplify1.6s

Counts

58 → 58

Iterations

Iter	Nodes
done	5007
4	3040
3	829
2	287
1	116
0	73

prune414.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.2b

localize33.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma x.re y.re (* x.im y.im))
16.3b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
30.5b	(sqrt (fma y.im y.im (* y.re y.re)))
30.5b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite9.0ms

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)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(fma x.re y.re (* x.im y.im))
166.0ms	(/ (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)))
62.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify3.1s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
5	4414
4	1335
3	532
2	242
1	138
0	90

prune638.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
1.3b	(fma x.re y.re (* x.im y.im))
16.3b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
30.5b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `fma-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def` `associate-/l/`

Counts

4 → 169

Calls

4 calls:

10.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (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)) (hypot y.im y.re))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
67.0ms	(fma x.re y.re (* x.im y.im))
137.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
54.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.0s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
3	3277
2	1006
1	458
0	228

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
1.3b	(fma x.re y.re (* x.im y.im))
16.3b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

8.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.0ms	(fma x.re y.re (* x.im y.im))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

series367.0ms

Counts

3 → 9

Calls

3 calls:

156.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
66.0ms	(fma x.re y.re (* x.im y.im))
145.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify2.2s

Counts

120 → 120

Iterations

Iter	Nodes
done	5406
3	3139
2	840
1	330
0	161

prune844.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

regimes502.0ms

Accuracy

32.5% (7.8b remaining)

Error of 13.6b against oracle of 5.8b and baseline of 17.4b

bsearch72.0ms

Steps

Iters	Range		Point
9	6.36185677957703e+145	5.205407902564929e+153	1.8016086380156584e+148
5	-2.2871888563215003e+52	-5.952772209436251e+51	-2.2512419148347823e+52

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	18

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

8459×

body

valid