Average Error: 15.0 → 0.0
Time: 1.5s
Precision: binary64
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]
↓
\[\frac{0.5}{y} + \frac{0.5}{x} \]
(FPCore (x y) :precision binary64 (/ (+ x y) (* (* x 2.0) y)))
↓
(FPCore (x y) :precision binary64 (+ (/ 0.5 y) (/ 0.5 x)))
double code(double x, double y) {
	return (x + y) / ((x * 2.0) * y);
}
↓
double code(double x, double y) {
	return (0.5 / y) + (0.5 / x);
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / ((x * 2.0d0) * y)
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (0.5d0 / y) + (0.5d0 / x)
end function

public static double code(double x, double y) {
	return (x + y) / ((x * 2.0) * y);
}
↓
public static double code(double x, double y) {
	return (0.5 / y) + (0.5 / x);
}

def code(x, y):
	return (x + y) / ((x * 2.0) * y)
↓
def code(x, y):
	return (0.5 / y) + (0.5 / x)

function code(x, y)
	return Float64(Float64(x + y) / Float64(Float64(x * 2.0) * y))
end
↓
function code(x, y)
	return Float64(Float64(0.5 / y) + Float64(0.5 / x))
end

function tmp = code(x, y)
	tmp = (x + y) / ((x * 2.0) * y);
end
↓
function tmp = code(x, y)
	tmp = (0.5 / y) + (0.5 / x);
end

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(N[(0.5 / y), $MachinePrecision] + N[(0.5 / x), $MachinePrecision]), $MachinePrecision]

\frac{x + y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{y} + \frac{0.5}{x}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.0
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y} \]

Derivation

  1. Initial program 15.0

    \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]

  2. Taylor expanded in x around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{x}} \]

  3. Simplified0.0

    \[\leadsto \color{blue}{\frac{0.5}{y} + \frac{0.5}{x}} \]

  4. Final simplification0.0

    \[\leadsto \frac{0.5}{y} + \frac{0.5}{x} \]

Reproduce

herbie shell --seed 2022150 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"
  :precision binary64

  :herbie-target
  (+ (/ 0.5 x) (/ 0.5 y))

  (/ (+ x y) (* (* x 2.0) y)))