Average Error: 3.7 → 1.3
Time: 11.2s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 1.018025094121265229501382308592741530739 \cdot 10^{-108}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z} \cdot \frac{\frac{\sqrt[3]{t}}{3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le 1.018025094121265229501382308592741530739 \cdot 10^{-108}:\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z} \cdot \frac{\frac{\sqrt[3]{t}}{3}}{y}\\

\mathbf{else}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r508784 = x;
        double r508785 = y;
        double r508786 = z;
        double r508787 = 3.0;
        double r508788 = r508786 * r508787;
        double r508789 = r508785 / r508788;
        double r508790 = r508784 - r508789;
        double r508791 = t;
        double r508792 = r508788 * r508785;
        double r508793 = r508791 / r508792;
        double r508794 = r508790 + r508793;
        return r508794;
}
↓
double f(double x, double y, double z, double t) {
        double r508795 = t;
        double r508796 = 1.0180250941212652e-108;
        bool r508797 = r508795 <= r508796;
        double r508798 = x;
        double r508799 = y;
        double r508800 = z;
        double r508801 = r508799 / r508800;
        double r508802 = 3.0;
        double r508803 = r508801 / r508802;
        double r508804 = r508798 - r508803;
        double r508805 = cbrt(r508795);
        double r508806 = r508805 * r508805;
        double r508807 = r508806 / r508800;
        double r508808 = r508805 / r508802;
        double r508809 = r508808 / r508799;
        double r508810 = r508807 * r508809;
        double r508811 = r508804 + r508810;
        double r508812 = r508800 * r508802;
        double r508813 = r508799 / r508812;
        double r508814 = r508798 - r508813;
        double r508815 = r508802 * r508799;
        double r508816 = r508800 * r508815;
        double r508817 = r508795 / r508816;
        double r508818 = r508814 + r508817;
        double r508819 = r508797 ? r508811 : r508818;
        return r508819;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.7
Target1.8
Herbie1.3
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if t < 1.0180250941212652e-108

    1. Initial program 4.9

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-/r*1.8

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}}\]
    4. Using strategy rm

    5. Applied associate-/r*1.8

      \[\leadsto \left(x - \color{blue}{\frac{\frac{y}{z}}{3}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity1.8

      \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{\color{blue}{1 \cdot y}}\]

    8. Applied add-cube-cbrt2.1

      \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}{z \cdot 3}}{1 \cdot y}\]

    9. Applied times-frac2.0

      \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\color{blue}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z} \cdot \frac{\sqrt[3]{t}}{3}}}{1 \cdot y}\]

    10. Applied times-frac1.4

      \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \color{blue}{\frac{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z}}{1} \cdot \frac{\frac{\sqrt[3]{t}}{3}}{y}}\]

    11. Simplified1.4

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

    if 1.0180250941212652e-108 < t

    1. Initial program 1.2

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-*l*1.2

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 1.018025094121265229501382308592741530739 \cdot 10^{-108}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z} \cdot \frac{\frac{\sqrt[3]{t}}{3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y))

  (+ (- x (/ y (* z 3))) (/ t (* (* z 3) y))))