Average Error: 14.6 → 0.0
Time: 5.0s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]
↓
\[\frac{0.5}{x} + \frac{0.5}{y}\]
\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}
↓
\frac{0.5}{x} + \frac{0.5}{y}
double f(double x, double y) {
        double r25215541 = x;
        double r25215542 = y;
        double r25215543 = r25215541 + r25215542;
        double r25215544 = 2.0;
        double r25215545 = r25215541 * r25215544;
        double r25215546 = r25215545 * r25215542;
        double r25215547 = r25215543 / r25215546;
        return r25215547;
}
↓
double f(double x, double y) {
        double r25215548 = 0.5;
        double r25215549 = x;
        double r25215550 = r25215548 / r25215549;
        double r25215551 = y;
        double r25215552 = r25215548 / r25215551;
        double r25215553 = r25215550 + r25215552;
        return r25215553;
}

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

Original14.6
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 14.6

    \[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]

  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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 +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)))