Average Error: 15.1 → 0.0
Time: 9.8s
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 r20796266 = x;
        double r20796267 = y;
        double r20796268 = r20796266 + r20796267;
        double r20796269 = 2.0;
        double r20796270 = r20796266 * r20796269;
        double r20796271 = r20796270 * r20796267;
        double r20796272 = r20796268 / r20796271;
        return r20796272;
}
↓
double f(double x, double y) {
        double r20796273 = 0.5;
        double r20796274 = y;
        double r20796275 = r20796273 / r20796274;
        double r20796276 = x;
        double r20796277 = r20796273 / r20796276;
        double r20796278 = r20796275 + r20796277;
        return r20796278;
}

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

Original15.1
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 15.1

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

  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 2019179 +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)))