| Alternative 1 | |
|---|---|
| Error | 50.7 |
| Cost | 7168 |
\[{\left(\left(-0.375 \cdot \frac{lo}{hi} - \frac{hi}{lo}\right) + -0.5\right)}^{2}
\]
Error
(FPCore (lo hi x) :precision binary64 (/ (- x lo) (- hi lo)))
(FPCore (lo hi x) :precision binary64 (/ (+ 1.0 (pow (/ (* hi (+ (/ hi lo) 1.0)) lo) 3.0)) (+ (* (/ hi lo) (/ hi lo)) (+ 1.0 (/ (* hi (- -1.0 (/ hi lo))) lo)))))
double code(double lo, double hi, double x) {
return (x - lo) / (hi - lo);
}
double code(double lo, double hi, double x) {
return (1.0 + pow(((hi * ((hi / lo) + 1.0)) / lo), 3.0)) / (((hi / lo) * (hi / lo)) + (1.0 + ((hi * (-1.0 - (hi / lo))) / lo)));
}
real(8) function code(lo, hi, x)
real(8), intent (in) :: lo
real(8), intent (in) :: hi
real(8), intent (in) :: x
code = (x - lo) / (hi - lo)
end function
real(8) function code(lo, hi, x)
real(8), intent (in) :: lo
real(8), intent (in) :: hi
real(8), intent (in) :: x
code = (1.0d0 + (((hi * ((hi / lo) + 1.0d0)) / lo) ** 3.0d0)) / (((hi / lo) * (hi / lo)) + (1.0d0 + ((hi * ((-1.0d0) - (hi / lo))) / lo)))
end function
public static double code(double lo, double hi, double x) {
return (x - lo) / (hi - lo);
}
public static double code(double lo, double hi, double x) {
return (1.0 + Math.pow(((hi * ((hi / lo) + 1.0)) / lo), 3.0)) / (((hi / lo) * (hi / lo)) + (1.0 + ((hi * (-1.0 - (hi / lo))) / lo)));
}
def code(lo, hi, x): return (x - lo) / (hi - lo)
def code(lo, hi, x): return (1.0 + math.pow(((hi * ((hi / lo) + 1.0)) / lo), 3.0)) / (((hi / lo) * (hi / lo)) + (1.0 + ((hi * (-1.0 - (hi / lo))) / lo)))
function code(lo, hi, x) return Float64(Float64(x - lo) / Float64(hi - lo)) end
function code(lo, hi, x) return Float64(Float64(1.0 + (Float64(Float64(hi * Float64(Float64(hi / lo) + 1.0)) / lo) ^ 3.0)) / Float64(Float64(Float64(hi / lo) * Float64(hi / lo)) + Float64(1.0 + Float64(Float64(hi * Float64(-1.0 - Float64(hi / lo))) / lo)))) end
function tmp = code(lo, hi, x) tmp = (x - lo) / (hi - lo); end
function tmp = code(lo, hi, x) tmp = (1.0 + (((hi * ((hi / lo) + 1.0)) / lo) ^ 3.0)) / (((hi / lo) * (hi / lo)) + (1.0 + ((hi * (-1.0 - (hi / lo))) / lo))); end
code[lo_, hi_, x_] := N[(N[(x - lo), $MachinePrecision] / N[(hi - lo), $MachinePrecision]), $MachinePrecision]
code[lo_, hi_, x_] := N[(N[(1.0 + N[Power[N[(N[(hi * N[(N[(hi / lo), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / lo), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(hi / lo), $MachinePrecision] * N[(hi / lo), $MachinePrecision]), $MachinePrecision] + N[(1.0 + N[(N[(hi * N[(-1.0 - N[(hi / lo), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / lo), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\frac{x - lo}{hi - lo}
\frac{1 + {\left(\frac{hi \cdot \left(\frac{hi}{lo} + 1\right)}{lo}\right)}^{3}}{\frac{hi}{lo} \cdot \frac{hi}{lo} + \left(1 + \frac{hi \cdot \left(-1 - \frac{hi}{lo}\right)}{lo}\right)}
Results
Initial program 62.0
Taylor expanded in lo around inf 64.0
Simplified51.9
Taylor expanded in x around 0 51.9
Simplified51.9
Applied egg-rr51.9
Taylor expanded in hi around 0 64.0
Simplified43.7
Final simplification43.7
| Alternative 1 | |
|---|---|
| Error | 50.7 |
| Cost | 7168 |
| Alternative 2 | |
|---|---|
| Error | 51.6 |
| Cost | 448 |
| Alternative 3 | |
|---|---|
| Error | 51.6 |
| Cost | 448 |
| Alternative 4 | |
|---|---|
| Error | 52.0 |
| Cost | 320 |
| Alternative 5 | |
|---|---|
| Error | 52.0 |
| Cost | 256 |
| Alternative 6 | |
|---|---|
| Error | 52.0 |
| Cost | 64 |
herbie shell --seed 2022291
(FPCore (lo hi x)
:name "(/ (- x lo) (- hi lo))"
:precision binary64
:pre (and (< lo -1e+308) (> hi 1e+308))
(/ (- x lo) (- hi lo)))