Average Error: 15.1 → 0.0
Time: 19.4s
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 r1043418 = x;
        double r1043419 = y;
        double r1043420 = r1043418 + r1043419;
        double r1043421 = 2.0;
        double r1043422 = r1043418 * r1043421;
        double r1043423 = r1043422 * r1043419;
        double r1043424 = r1043420 / r1043423;
        return r1043424;
}
↓
double f(double x, double y) {
        double r1043425 = 0.5;
        double r1043426 = y;
        double r1043427 = r1043425 / r1043426;
        double r1043428 = x;
        double r1043429 = r1043425 / r1043428;
        double r1043430 = r1043427 + r1043429;
        return r1043430;
}

Error

Bits error versus x

Bits error versus y

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Results

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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. Simplified15.2

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(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)))