Details

sample33.0ms

Algorithm

intervals

Results

21.0ms

275×

body

valid

simplify27.0ms

Counts: 1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize18.0ms

Local error

Found 2 expressions with local error:

24.2b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.8b	(fma x.re y.re (* x.im y.im))

rewrite6.0ms

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:

Slowest

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

series166.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

121.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
45.0ms	(fma x.re y.re (* x.im y.im))

simplify1.1s

Counts: 47 → 47

prune695.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.8b

localize29.0ms

Local error

Found 4 expressions with local error:

31.7b	(sqrt (fma y.im y.im (* y.re y.re)))
31.7b	(sqrt (fma y.im y.im (* y.re y.re)))
15.9b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.8b	(fma x.re y.re (* x.im y.im))

rewrite8.0ms

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:

Slowest

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

series325.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
65.0ms	(fma x.re y.re (* x.im y.im))
65.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
55.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.1s

Counts: 99 → 99

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.7b

localize35.0ms

Local error

Found 4 expressions with local error:

31.7b	(sqrt (fma y.im y.im (* y.re y.re)))
15.9b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.8b	(fma x.re y.re (* x.im y.im))
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
96×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
25×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `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 → 179

Calls

4 calls:

Slowest

9.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
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)))
0.0ms	(fma x.re y.re (* x.im y.im))

series435.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

180.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
155.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
56.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
44.0ms	(fma x.re y.re (* x.im y.im))

simplify1.6s

Counts: 191 → 191

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 3 expressions with local error:

15.9b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
0.8b	(fma x.re y.re (* x.im y.im))
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))

rewrite19.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`fma-udef` `associate-/l/`

Counts

3 → 114

Calls

3 calls:

Slowest

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

series300.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

130.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
128.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
43.0ms	(fma x.re y.re (* x.im y.im))

simplify1.2s

Counts: 123 → 123

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

regimes366.0ms

Accuracy

36.1% (6.9b remaining)

Error of 12.6b against oracle of 5.7b and baseline of 16.5b

bsearch147.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s

8497×

body

valid