Average Error: 14.7 → 0.2
Time: 29.4s
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 r451511 = x;
        double r451512 = 2.0;
        double r451513 = r451511 * r451512;
        double r451514 = y;
        double r451515 = r451513 * r451514;
        double r451516 = r451511 - r451514;
        double r451517 = r451515 / r451516;
        return r451517;
}
↓
double f(double x, double y) {
        double r451518 = 1.0;
        double r451519 = 0.5;
        double r451520 = y;
        double r451521 = r451519 / r451520;
        double r451522 = x;
        double r451523 = r451519 / r451522;
        double r451524 = r451521 - r451523;
        double r451525 = r451518 / r451524;
        return r451525;
}

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

Original14.7
Target0.4
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 14.7

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

  3. Applied associate-/l*7.9

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

  4. Simplified7.9

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

  6. Applied clear-num8.0

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

  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 2019212 
(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)))