Average Error: 14.9 → 0.0
Time: 25.4s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{x} + \frac{0.5}{y}\]
\frac{x + y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{x} + \frac{0.5}{y}
double f(double x, double y) {
        double r25378092 = x;
        double r25378093 = y;
        double r25378094 = r25378092 + r25378093;
        double r25378095 = 2.0;
        double r25378096 = r25378092 * r25378095;
        double r25378097 = r25378096 * r25378093;
        double r25378098 = r25378094 / r25378097;
        return r25378098;
}
↓
double f(double x, double y) {
        double r25378099 = 0.5;
        double r25378100 = x;
        double r25378101 = r25378099 / r25378100;
        double r25378102 = y;
        double r25378103 = r25378099 / r25378102;
        double r25378104 = r25378101 + r25378103;
        return r25378104;
}

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

Original14.9
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 14.9

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

  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

    \[\leadsto \frac{0.5}{x} + \frac{0.5}{y}\]

Reproduce

herbie shell --seed 2019200 +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)))