Average Error: 15.2 → 0.0
Time: 8.8s
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 r75821071 = x;
        double r75821072 = y;
        double r75821073 = r75821071 + r75821072;
        double r75821074 = 2.0;
        double r75821075 = r75821071 * r75821074;
        double r75821076 = r75821075 * r75821072;
        double r75821077 = r75821073 / r75821076;
        return r75821077;
}
↓
double f(double x, double y) {
        double r75821078 = 0.5;
        double r75821079 = y;
        double r75821080 = r75821078 / r75821079;
        double r75821081 = x;
        double r75821082 = r75821078 / r75821081;
        double r75821083 = r75821080 + r75821082;
        return r75821083;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 15.2

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

  2. Taylor expanded around 0 0.0

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

  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 2019173 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"

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

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