Average Error: 15.0 → 0.2
Time: 13.4s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\frac{1}{\frac{0.5}{y} - \frac{0.5}{x}}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\frac{1}{\frac{0.5}{y} - \frac{0.5}{x}}
double f(double x, double y) {
        double r471884 = x;
        double r471885 = 2.0;
        double r471886 = r471884 * r471885;
        double r471887 = y;
        double r471888 = r471886 * r471887;
        double r471889 = r471884 - r471887;
        double r471890 = r471888 / r471889;
        return r471890;
}
↓
double f(double x, double y) {
        double r471891 = 1.0;
        double r471892 = 0.5;
        double r471893 = y;
        double r471894 = r471892 / r471893;
        double r471895 = x;
        double r471896 = r471892 / r471895;
        double r471897 = r471894 - r471896;
        double r471898 = r471891 / r471897;
        return r471898;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.0
Target0.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -1.721044263414944729490876394165887012892 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Initial program 15.0

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

  3. Applied associate-/l*7.1

    \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}}\]

  4. Simplified7.1

    \[\leadsto \frac{x \cdot 2}{\color{blue}{\frac{x}{y} - 1}}\]
  5. Using strategy rm

  6. Applied clear-num7.2

    \[\leadsto \color{blue}{\frac{1}{\frac{\frac{x}{y} - 1}{x \cdot 2}}}\]

  7. Taylor expanded around 0 0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

    \[\leadsto \frac{1}{\frac{0.5}{y} - \frac{0.5}{x}}\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e81) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564432) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y)))

  (/ (* (* x 2) y) (- x y)))