Average Error: 3.9 → 0.3
Time: 13.3s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le -2.315641800986653731087017149548046290874:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + t \cdot \frac{\frac{1}{y}}{3 \cdot z}\\ \mathbf{elif}\;z \cdot 3 \le 2.181965382420920083950531709255992849268 \cdot 10^{-43}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]
\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 -2.315641800986653731087017149548046290874:\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + t \cdot \frac{\frac{1}{y}}{3 \cdot z}\\

\mathbf{elif}\;z \cdot 3 \le 2.181965382420920083950531709255992849268 \cdot 10^{-43}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\

\mathbf{else}:\\
\;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r496797 = x;
        double r496798 = y;
        double r496799 = z;
        double r496800 = 3.0;
        double r496801 = r496799 * r496800;
        double r496802 = r496798 / r496801;
        double r496803 = r496797 - r496802;
        double r496804 = t;
        double r496805 = r496801 * r496798;
        double r496806 = r496804 / r496805;
        double r496807 = r496803 + r496806;
        return r496807;
}
↓
double f(double x, double y, double z, double t) {
        double r496808 = z;
        double r496809 = 3.0;
        double r496810 = r496808 * r496809;
        double r496811 = -2.3156418009866537;
        bool r496812 = r496810 <= r496811;
        double r496813 = x;
        double r496814 = y;
        double r496815 = r496814 / r496808;
        double r496816 = r496815 / r496809;
        double r496817 = r496813 - r496816;
        double r496818 = t;
        double r496819 = 1.0;
        double r496820 = r496819 / r496814;
        double r496821 = r496809 * r496808;
        double r496822 = r496820 / r496821;
        double r496823 = r496818 * r496822;
        double r496824 = r496817 + r496823;
        double r496825 = 2.18196538242092e-43;
        bool r496826 = r496810 <= r496825;
        double r496827 = r496814 / r496810;
        double r496828 = r496813 - r496827;
        double r496829 = r496818 / r496814;
        double r496830 = r496829 / r496810;
        double r496831 = r496828 + r496830;
        double r496832 = r496819 / r496808;
        double r496833 = r496814 / r496809;
        double r496834 = r496832 * r496833;
        double r496835 = r496813 - r496834;
        double r496836 = r496810 * r496814;
        double r496837 = r496818 / r496836;
        double r496838 = r496835 + r496837;
        double r496839 = r496826 ? r496831 : r496838;
        double r496840 = r496812 ? r496824 : r496839;
        return r496840;
}

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

Original3.9
Target1.9
Herbie0.3
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if (* z 3.0) < -2.3156418009866537

    1. Initial program 0.4

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

    3. Applied add-cube-cbrt0.6

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

    4. Applied times-frac2.0

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

    6. Applied div-inv2.0

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

    7. Applied associate-*r*1.4

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

    8. Simplified1.2

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

    10. Applied associate-/r*1.1

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

    12. Applied div-inv1.1

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

    13. Applied associate-*l*0.3

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

    14. Simplified0.3

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

    if -2.3156418009866537 < (* z 3.0) < 2.18196538242092e-43

    1. Initial program 12.1

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

    3. Applied add-cube-cbrt12.3

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

    4. Applied times-frac1.1

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

    6. Applied associate-*l/0.6

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

    7. Simplified0.3

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

    if 2.18196538242092e-43 < (* z 3.0)

    1. Initial program 0.3

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

    3. Applied *-un-lft-identity0.3

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

    4. Applied times-frac0.4

      \[\leadsto \left(x - \color{blue}{\frac{1}{z} \cdot \frac{y}{3}}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le -2.315641800986653731087017149548046290874:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + t \cdot \frac{\frac{1}{y}}{3 \cdot z}\\ \mathbf{elif}\;z \cdot 3 \le 2.181965382420920083950531709255992849268 \cdot 10^{-43}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))))