Average Error: 15.5 → 0.0
Time: 25.1s
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 r28139973 = x;
        double r28139974 = y;
        double r28139975 = r28139973 - r28139974;
        double r28139976 = 2.0;
        double r28139977 = r28139973 * r28139976;
        double r28139978 = r28139977 * r28139974;
        double r28139979 = r28139975 / r28139978;
        return r28139979;
}
↓
double f(double x, double y) {
        double r28139980 = 0.5;
        double r28139981 = y;
        double r28139982 = r28139980 / r28139981;
        double r28139983 = x;
        double r28139984 = r28139980 / r28139983;
        double r28139985 = r28139982 - r28139984;
        return r28139985;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019192 
(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)))