?

Average Error: 62.0 → 52.0
Time: 17.2s
Precision: binary64
Cost: 256

?

\[lo < -1 \cdot 10^{+308} \land hi > 10^{+308}\]
\[\frac{x - lo}{hi - lo} \]
↓
\[-\frac{lo}{hi} \]
(FPCore (lo hi x) :precision binary64 (/ (- x lo) (- hi lo)))
↓
(FPCore (lo hi x) :precision binary64 (- (/ lo hi)))
double code(double lo, double hi, double x) {
	return (x - lo) / (hi - lo);
}
↓
double code(double lo, double hi, double x) {
	return -(lo / hi);
}

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 = -(lo / hi)
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 -(lo / hi);
}

def code(lo, hi, x):
	return (x - lo) / (hi - lo)
↓
def code(lo, hi, x):
	return -(lo / hi)

function code(lo, hi, x)
	return Float64(Float64(x - lo) / Float64(hi - lo))
end
↓
function code(lo, hi, x)
	return Float64(-Float64(lo / hi))
end

function tmp = code(lo, hi, x)
	tmp = (x - lo) / (hi - lo);
end
↓
function tmp = code(lo, hi, x)
	tmp = -(lo / hi);
end

code[lo_, hi_, x_] := N[(N[(x - lo), $MachinePrecision] / N[(hi - lo), $MachinePrecision]), $MachinePrecision]
↓
code[lo_, hi_, x_] := (-N[(lo / hi), $MachinePrecision])

\frac{x - lo}{hi - lo}
↓
-\frac{lo}{hi}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 62.0

    \[\frac{x - lo}{hi - lo} \]

  2. Taylor expanded in hi around inf 52.0

    \[\leadsto \color{blue}{\frac{x - lo}{hi}} \]

  3. Taylor expanded in x around 0 52.0

    \[\leadsto \color{blue}{-1 \cdot \frac{lo}{hi}} \]

  4. Simplified52.0

    \[\leadsto \color{blue}{-\frac{lo}{hi}} \]
    Proof

    [Start]52.0

    \[ -1 \cdot \frac{lo}{hi} \]

    rational.json-simplify-2 [=>]52.0

    \[ \color{blue}{\frac{lo}{hi} \cdot -1} \]

    rational.json-simplify-9 [=>]52.0

    \[ \color{blue}{-\frac{lo}{hi}} \]

  5. Final simplification52.0

    \[\leadsto -\frac{lo}{hi} \]

Alternatives

Alternative 1
Error52.0
Cost64
\[1 \]

Error

Reproduce?

herbie shell --seed 2023069 
(FPCore (lo hi x)
  :name "xlohi (overflows)"
  :precision binary64
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))