Average Error: 0.0 → 0.0
Time: 1.6s
Precision: binary64
\[\frac{\left|x - y\right|}{\left|y\right|} \]
↓
\[\left|\frac{y - x}{y}\right| \]
(FPCore (x y) :precision binary64 (/ (fabs (- x y)) (fabs y)))
↓
(FPCore (x y) :precision binary64 (fabs (/ (- y x) y)))
double code(double x, double y) {
	return fabs((x - y)) / fabs(y);
}
↓
double code(double x, double y) {
	return fabs(((y - x) / y));
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = abs((x - y)) / abs(y)
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = abs(((y - x) / y))
end function

public static double code(double x, double y) {
	return Math.abs((x - y)) / Math.abs(y);
}
↓
public static double code(double x, double y) {
	return Math.abs(((y - x) / y));
}

def code(x, y):
	return math.fabs((x - y)) / math.fabs(y)
↓
def code(x, y):
	return math.fabs(((y - x) / y))

function code(x, y)
	return Float64(abs(Float64(x - y)) / abs(y))
end
↓
function code(x, y)
	return abs(Float64(Float64(y - x) / y))
end

function tmp = code(x, y)
	tmp = abs((x - y)) / abs(y);
end
↓
function tmp = code(x, y)
	tmp = abs(((y - x) / y));
end

code[x_, y_] := N[(N[Abs[N[(x - y), $MachinePrecision]], $MachinePrecision] / N[Abs[y], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[Abs[N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision]

\frac{\left|x - y\right|}{\left|y\right|}
↓
\left|\frac{y - x}{y}\right|

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{\left|x - y\right|}{\left|y\right|} \]

  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{\left|\frac{y - x}{y}\right|} \]

  3. Final simplification0.0

    \[\leadsto \left|\frac{y - x}{y}\right| \]

Reproduce

herbie shell --seed 2022150 
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))