?

Average Error: 15.2 → 0.0
Time: 47.9s
Precision: binary64
Cost: 448

?

\[\frac{x - y}{\left(x \cdot 2\right) \cdot y} \]
↓
\[\frac{0.5}{y} + \frac{-0.5}{x} \]
(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?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.2
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x} \]

Derivation?

  1. Initial program 15.2

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

  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

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

Alternatives

Alternative 1
Error17.1
Cost984
\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+101}:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+69}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-13}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{-86}:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{x}\\ \end{array} \]
Alternative 2
Error31.2
Cost192
\[\frac{-0.5}{x} \]

Error

Reproduce?

herbie shell --seed 2023033 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"
  :precision binary64

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

  (/ (- x y) (* (* x 2.0) y)))