Average Error: 3.9 → 0.3
Time: 13.4s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le -2.315641800986653731087017149548046290874:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + t \cdot \frac{\frac{1}{y}}{3 \cdot z}\\ \mathbf{elif}\;z \cdot 3 \le 2.181965382420920083950531709255992849268 \cdot 10^{-43}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]
\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 r460677 = x;
        double r460678 = y;
        double r460679 = z;
        double r460680 = 3.0;
        double r460681 = r460679 * r460680;
        double r460682 = r460678 / r460681;
        double r460683 = r460677 - r460682;
        double r460684 = t;
        double r460685 = r460681 * r460678;
        double r460686 = r460684 / r460685;
        double r460687 = r460683 + r460686;
        return r460687;
}
↓
double f(double x, double y, double z, double t) {
        double r460688 = z;
        double r460689 = 3.0;
        double r460690 = r460688 * r460689;
        double r460691 = -2.3156418009866537;
        bool r460692 = r460690 <= r460691;
        double r460693 = x;
        double r460694 = y;
        double r460695 = r460694 / r460688;
        double r460696 = r460695 / r460689;
        double r460697 = r460693 - r460696;
        double r460698 = t;
        double r460699 = 1.0;
        double r460700 = r460699 / r460694;
        double r460701 = r460689 * r460688;
        double r460702 = r460700 / r460701;
        double r460703 = r460698 * r460702;
        double r460704 = r460697 + r460703;
        double r460705 = 2.18196538242092e-43;
        bool r460706 = r460690 <= r460705;
        double r460707 = r460694 / r460690;
        double r460708 = r460693 - r460707;
        double r460709 = r460698 / r460694;
        double r460710 = r460709 / r460690;
        double r460711 = r460708 + r460710;
        double r460712 = r460699 / r460688;
        double r460713 = r460694 / r460689;
        double r460714 = r460712 * r460713;
        double r460715 = r460693 - r460714;
        double r460716 = r460690 * r460694;
        double r460717 = r460698 / r460716;
        double r460718 = r460715 + r460717;
        double r460719 = r460706 ? r460711 : r460718;
        double r460720 = r460692 ? r460704 : r460719;
        return r460720;
}

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))))