Average Error: 3.7 → 0.9
Time: 4.4s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le -1.16964350915532777 \cdot 10^{116}:\\ \;\;\;\;\left(x - \frac{\frac{\frac{y}{z}}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\sqrt[3]{3}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{elif}\;z \cdot 3 \le 1.52241256667558003 \cdot 10^{-52}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot 3 \le -1.16964350915532777 \cdot 10^{116}:\\
\;\;\;\;\left(x - \frac{\frac{\frac{y}{z}}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\sqrt[3]{3}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\

\mathbf{elif}\;z \cdot 3 \le 1.52241256667558003 \cdot 10^{-52}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{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 r833803 = x;
        double r833804 = y;
        double r833805 = z;
        double r833806 = 3.0;
        double r833807 = r833805 * r833806;
        double r833808 = r833804 / r833807;
        double r833809 = r833803 - r833808;
        double r833810 = t;
        double r833811 = r833807 * r833804;
        double r833812 = r833810 / r833811;
        double r833813 = r833809 + r833812;
        return r833813;
}
↓
double f(double x, double y, double z, double t) {
        double r833814 = z;
        double r833815 = 3.0;
        double r833816 = r833814 * r833815;
        double r833817 = -1.1696435091553278e+116;
        bool r833818 = r833816 <= r833817;
        double r833819 = x;
        double r833820 = y;
        double r833821 = r833820 / r833814;
        double r833822 = cbrt(r833815);
        double r833823 = r833822 * r833822;
        double r833824 = r833821 / r833823;
        double r833825 = r833824 / r833822;
        double r833826 = r833819 - r833825;
        double r833827 = t;
        double r833828 = r833827 / r833816;
        double r833829 = r833828 / r833820;
        double r833830 = r833826 + r833829;
        double r833831 = 1.52241256667558e-52;
        bool r833832 = r833816 <= r833831;
        double r833833 = r833820 / r833816;
        double r833834 = r833819 - r833833;
        double r833835 = 1.0;
        double r833836 = r833835 / r833816;
        double r833837 = r833827 / r833820;
        double r833838 = r833836 * r833837;
        double r833839 = r833834 + r833838;
        double r833840 = r833815 * r833820;
        double r833841 = r833814 * r833840;
        double r833842 = r833827 / r833841;
        double r833843 = r833834 + r833842;
        double r833844 = r833832 ? r833839 : r833843;
        double r833845 = r833818 ? r833830 : r833844;
        return r833845;
}

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
Herbie0.9
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if (* z 3.0) < -1.1696435091553278e+116

    1. Initial program 0.7

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

    3. Applied associate-/r*1.1

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

    5. Applied associate-/r*1.1

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

    7. Applied add-cube-cbrt1.1

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

    8. Applied associate-/r*1.2

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

    if -1.1696435091553278e+116 < (* z 3.0) < 1.52241256667558e-52

    1. Initial program 8.3

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

    3. Applied *-un-lft-identity8.3

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

    4. Applied times-frac1.1

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

    if 1.52241256667558e-52 < (* z 3.0)

    1. Initial program 0.6

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

    3. Applied associate-*l*0.5

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le -1.16964350915532777 \cdot 10^{116}:\\ \;\;\;\;\left(x - \frac{\frac{\frac{y}{z}}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\sqrt[3]{3}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{elif}\;z \cdot 3 \le 1.52241256667558003 \cdot 10^{-52}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020021 
(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))))