Average Error: 3.6 → 0.9
Time: 25.5s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.876078776862118321950943559866525589816 \cdot 10^{147}:\\ \;\;\;\;\frac{\frac{\frac{t}{z}}{3}}{y} + \left(x - \frac{y}{3 \cdot z}\right)\\ \mathbf{elif}\;z \le 101100649468898151561565306880:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}} + \left(x - \frac{y}{3 \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(3 \cdot z\right) \cdot y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.876078776862118321950943559866525589816 \cdot 10^{147}:\\
\;\;\;\;\frac{\frac{\frac{t}{z}}{3}}{y} + \left(x - \frac{y}{3 \cdot z}\right)\\

\mathbf{elif}\;z \le 101100649468898151561565306880:\\
\;\;\;\;\frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}} + \left(x - \frac{y}{3 \cdot z}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r35214880 = x;
        double r35214881 = y;
        double r35214882 = z;
        double r35214883 = 3.0;
        double r35214884 = r35214882 * r35214883;
        double r35214885 = r35214881 / r35214884;
        double r35214886 = r35214880 - r35214885;
        double r35214887 = t;
        double r35214888 = r35214884 * r35214881;
        double r35214889 = r35214887 / r35214888;
        double r35214890 = r35214886 + r35214889;
        return r35214890;
}
↓
double f(double x, double y, double z, double t) {
        double r35214891 = z;
        double r35214892 = -1.8760787768621183e+147;
        bool r35214893 = r35214891 <= r35214892;
        double r35214894 = t;
        double r35214895 = r35214894 / r35214891;
        double r35214896 = 3.0;
        double r35214897 = r35214895 / r35214896;
        double r35214898 = y;
        double r35214899 = r35214897 / r35214898;
        double r35214900 = x;
        double r35214901 = r35214896 * r35214891;
        double r35214902 = r35214898 / r35214901;
        double r35214903 = r35214900 - r35214902;
        double r35214904 = r35214899 + r35214903;
        double r35214905 = 1.0110064946889815e+29;
        bool r35214906 = r35214891 <= r35214905;
        double r35214907 = 1.0;
        double r35214908 = r35214907 / r35214891;
        double r35214909 = r35214894 / r35214896;
        double r35214910 = r35214898 / r35214909;
        double r35214911 = r35214908 / r35214910;
        double r35214912 = r35214911 + r35214903;
        double r35214913 = r35214898 / r35214891;
        double r35214914 = r35214913 / r35214896;
        double r35214915 = r35214900 - r35214914;
        double r35214916 = r35214901 * r35214898;
        double r35214917 = r35214894 / r35214916;
        double r35214918 = r35214915 + r35214917;
        double r35214919 = r35214906 ? r35214912 : r35214918;
        double r35214920 = r35214893 ? r35214904 : r35214919;
        return r35214920;
}

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

Original3.6
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 < -1.8760787768621183e+147

    1. Initial program 0.5

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    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 *-un-lft-identity1.1

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

    6. Applied associate-/r*1.1

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

    7. Simplified1.0

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

    if -1.8760787768621183e+147 < z < 1.0110064946889815e+29

    1. Initial program 6.5

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

    3. Applied associate-/r*2.4

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

    5. Applied *-un-lft-identity2.4

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

    6. Applied times-frac2.4

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

    7. Applied associate-/l*1.1

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

    if 1.0110064946889815e+29 < z

    1. Initial program 0.5

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

    3. Applied associate-/r*0.5

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.876078776862118321950943559866525589816 \cdot 10^{147}:\\ \;\;\;\;\frac{\frac{\frac{t}{z}}{3}}{y} + \left(x - \frac{y}{3 \cdot z}\right)\\ \mathbf{elif}\;z \le 101100649468898151561565306880:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}} + \left(x - \frac{y}{3 \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(3 \cdot z\right) \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))