Average Error: 15.3 → 1.4
Time: 4.2s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -0.0:\\ \;\;\;\;\left(\left(x \cdot 2\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{x - y}}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 1.5055267344693184 \cdot 10^{-5}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -0.0:\\
\;\;\;\;\left(\left(x \cdot 2\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{x - y}}\\

\mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 1.5055267344693184 \cdot 10^{-5}:\\
\;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\

\end{array}
double f(double x, double y) {
        double r617722 = x;
        double r617723 = 2.0;
        double r617724 = r617722 * r617723;
        double r617725 = y;
        double r617726 = r617724 * r617725;
        double r617727 = r617722 - r617725;
        double r617728 = r617726 / r617727;
        return r617728;
}
↓
double f(double x, double y) {
        double r617729 = x;
        double r617730 = 2.0;
        double r617731 = r617729 * r617730;
        double r617732 = y;
        double r617733 = r617731 * r617732;
        double r617734 = r617729 - r617732;
        double r617735 = r617733 / r617734;
        double r617736 = -0.0;
        bool r617737 = r617735 <= r617736;
        double r617738 = cbrt(r617732);
        double r617739 = r617738 * r617738;
        double r617740 = cbrt(r617734);
        double r617741 = r617740 * r617740;
        double r617742 = r617739 / r617741;
        double r617743 = r617731 * r617742;
        double r617744 = r617738 / r617740;
        double r617745 = r617743 * r617744;
        double r617746 = 1.5055267344693184e-05;
        bool r617747 = r617735 <= r617746;
        double r617748 = r617734 / r617732;
        double r617749 = r617731 / r617748;
        double r617750 = r617747 ? r617735 : r617749;
        double r617751 = r617737 ? r617745 : r617750;
        return r617751;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.3
Target0.4
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* (* x 2.0) y) (- x y)) < -0.0

    1. Initial program 19.5

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

    3. Applied *-un-lft-identity19.5

      \[\leadsto \frac{\left(x \cdot 2\right) \cdot y}{\color{blue}{1 \cdot \left(x - y\right)}}\]

    4. Applied times-frac6.3

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

    5. Simplified6.3

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

    7. Applied add-cube-cbrt7.5

      \[\leadsto \left(x \cdot 2\right) \cdot \frac{y}{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}\]

    8. Applied add-cube-cbrt6.9

      \[\leadsto \left(x \cdot 2\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}\]

    9. Applied times-frac6.9

      \[\leadsto \left(x \cdot 2\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{x - y}}\right)}\]

    10. Applied associate-*r*2.3

      \[\leadsto \color{blue}{\left(\left(x \cdot 2\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{x - y}}}\]

    if -0.0 < (/ (* (* x 2.0) y) (- x y)) < 1.5055267344693184e-05

    1. Initial program 0.4

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]

    if 1.5055267344693184e-05 < (/ (* (* x 2.0) y) (- x y))

    1. Initial program 31.5

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

    3. Applied associate-/l*0.1

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le -0.0:\\ \;\;\;\;\left(\left(x \cdot 2\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{x - y}}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \le 1.5055267344693184 \cdot 10^{-5}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564432) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y)))

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