Average Error: 15.1 → 0.0
Time: 9.0s
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 r26414397 = x;
        double r26414398 = y;
        double r26414399 = r26414397 + r26414398;
        double r26414400 = 2.0;
        double r26414401 = r26414397 * r26414400;
        double r26414402 = r26414401 * r26414398;
        double r26414403 = r26414399 / r26414402;
        return r26414403;
}
↓
double f(double x, double y) {
        double r26414404 = 0.5;
        double r26414405 = y;
        double r26414406 = r26414404 / r26414405;
        double r26414407 = x;
        double r26414408 = r26414404 / r26414407;
        double r26414409 = r26414406 + r26414408;
        return r26414409;
}

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. 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 
(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)))