Average Error: 15.5 → 0.0
Time: 21.3s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{y} - \frac{0.5}{x}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{y} - \frac{0.5}{x}
double f(double x, double y) {
        double r341075 = x;
        double r341076 = y;
        double r341077 = r341075 - r341076;
        double r341078 = 2.0;
        double r341079 = r341075 * r341078;
        double r341080 = r341079 * r341076;
        double r341081 = r341077 / r341080;
        return r341081;
}
↓
double f(double x, double y) {
        double r341082 = 0.5;
        double r341083 = y;
        double r341084 = r341082 / r341083;
        double r341085 = x;
        double r341086 = r341082 / r341085;
        double r341087 = r341084 - r341086;
        return r341087;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original15.5
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.5

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

  2. Taylor expanded 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 2019199 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"

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

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