Average Error: 15.2 → 0.0
Time: 2.1s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{1}{2 \cdot y} - \frac{1}{x \cdot 2}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{1}{2 \cdot y} - \frac{1}{x \cdot 2}
double f(double x, double y) {
        double r536106 = x;
        double r536107 = y;
        double r536108 = r536106 - r536107;
        double r536109 = 2.0;
        double r536110 = r536106 * r536109;
        double r536111 = r536110 * r536107;
        double r536112 = r536108 / r536111;
        return r536112;
}
↓
double f(double x, double y) {
        double r536113 = 1.0;
        double r536114 = 2.0;
        double r536115 = y;
        double r536116 = r536114 * r536115;
        double r536117 = r536113 / r536116;
        double r536118 = x;
        double r536119 = r536118 * r536114;
        double r536120 = r536113 / r536119;
        double r536121 = r536117 - r536120;
        return r536121;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.2
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. Using strategy rm

  3. Applied div-sub15.2

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

  4. Simplified11.3

    \[\leadsto \color{blue}{\frac{1}{2 \cdot y}} - \frac{y}{\left(x \cdot 2\right) \cdot y}\]

  5. Simplified0.0

    \[\leadsto \frac{1}{2 \cdot y} - \color{blue}{\frac{1}{x \cdot 2}}\]

  6. Final simplification0.0

    \[\leadsto \frac{1}{2 \cdot y} - \frac{1}{x \cdot 2}\]

Reproduce

herbie shell --seed 2019356 
(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) y)))