Average Error: 14.3 → 0.1
Time: 10.4s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -28977.221790386797:\\ \;\;\;\;\frac{\frac{y + x}{2.0}}{y} \cdot \frac{1}{x}\\ \mathbf{elif}\;y \le 3.49698992568305 \cdot 10^{-34}:\\ \;\;\;\;\frac{\frac{y + x}{2.0 \cdot x}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y + x}{2.0}}{y} \cdot \frac{1}{x}\\ \end{array}\]
\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -28977.221790386797:\\
\;\;\;\;\frac{\frac{y + x}{2.0}}{y} \cdot \frac{1}{x}\\

\mathbf{elif}\;y \le 3.49698992568305 \cdot 10^{-34}:\\
\;\;\;\;\frac{\frac{y + x}{2.0 \cdot x}}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{y + x}{2.0}}{y} \cdot \frac{1}{x}\\

\end{array}
double f(double x, double y) {
        double r24536451 = x;
        double r24536452 = y;
        double r24536453 = r24536451 + r24536452;
        double r24536454 = 2.0;
        double r24536455 = r24536451 * r24536454;
        double r24536456 = r24536455 * r24536452;
        double r24536457 = r24536453 / r24536456;
        return r24536457;
}
↓
double f(double x, double y) {
        double r24536458 = y;
        double r24536459 = -28977.221790386797;
        bool r24536460 = r24536458 <= r24536459;
        double r24536461 = x;
        double r24536462 = r24536458 + r24536461;
        double r24536463 = 2.0;
        double r24536464 = r24536462 / r24536463;
        double r24536465 = r24536464 / r24536458;
        double r24536466 = 1.0;
        double r24536467 = r24536466 / r24536461;
        double r24536468 = r24536465 * r24536467;
        double r24536469 = 3.49698992568305e-34;
        bool r24536470 = r24536458 <= r24536469;
        double r24536471 = r24536463 * r24536461;
        double r24536472 = r24536462 / r24536471;
        double r24536473 = r24536472 / r24536458;
        double r24536474 = r24536470 ? r24536473 : r24536468;
        double r24536475 = r24536460 ? r24536468 : r24536474;
        return r24536475;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.3
Target0.0
Herbie0.1
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -28977.221790386797 or 3.49698992568305e-34 < y

    1. Initial program 14.3

      \[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-/r*14.6

      \[\leadsto \color{blue}{\frac{\frac{x + y}{x \cdot 2.0}}{y}}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity14.6

      \[\leadsto \frac{\frac{x + y}{x \cdot 2.0}}{\color{blue}{1 \cdot y}}\]

    6. Applied *-un-lft-identity14.6

      \[\leadsto \frac{\frac{\color{blue}{1 \cdot \left(x + y\right)}}{x \cdot 2.0}}{1 \cdot y}\]

    7. Applied times-frac14.6

      \[\leadsto \frac{\color{blue}{\frac{1}{x} \cdot \frac{x + y}{2.0}}}{1 \cdot y}\]

    8. Applied times-frac0.2

      \[\leadsto \color{blue}{\frac{\frac{1}{x}}{1} \cdot \frac{\frac{x + y}{2.0}}{y}}\]

    9. Simplified0.2

      \[\leadsto \color{blue}{\frac{1}{x}} \cdot \frac{\frac{x + y}{2.0}}{y}\]

    if -28977.221790386797 < y < 3.49698992568305e-34

    1. Initial program 14.4

      \[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-/r*0.1

      \[\leadsto \color{blue}{\frac{\frac{x + y}{x \cdot 2.0}}{y}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -28977.221790386797:\\ \;\;\;\;\frac{\frac{y + x}{2.0}}{y} \cdot \frac{1}{x}\\ \mathbf{elif}\;y \le 3.49698992568305 \cdot 10^{-34}:\\ \;\;\;\;\frac{\frac{y + x}{2.0 \cdot x}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y + x}{2.0}}{y} \cdot \frac{1}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(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)))