Average Error: 3.4 → 2.0
Time: 11.9s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le 2.429085854700127248317880955221217421232 \cdot 10^{93}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]
\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 2.429085854700127248317880955221217421232 \cdot 10^{93}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{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 r751769 = x;
        double r751770 = y;
        double r751771 = z;
        double r751772 = 3.0;
        double r751773 = r751771 * r751772;
        double r751774 = r751770 / r751773;
        double r751775 = r751769 - r751774;
        double r751776 = t;
        double r751777 = r751773 * r751770;
        double r751778 = r751776 / r751777;
        double r751779 = r751775 + r751778;
        return r751779;
}
↓
double f(double x, double y, double z, double t) {
        double r751780 = z;
        double r751781 = 3.0;
        double r751782 = r751780 * r751781;
        double r751783 = 2.4290858547001272e+93;
        bool r751784 = r751782 <= r751783;
        double r751785 = x;
        double r751786 = y;
        double r751787 = r751786 / r751782;
        double r751788 = r751785 - r751787;
        double r751789 = 1.0;
        double r751790 = r751789 / r751780;
        double r751791 = t;
        double r751792 = r751791 / r751781;
        double r751793 = r751786 / r751792;
        double r751794 = r751790 / r751793;
        double r751795 = r751788 + r751794;
        double r751796 = r751786 / r751781;
        double r751797 = r751790 * r751796;
        double r751798 = r751785 - r751797;
        double r751799 = r751782 * r751786;
        double r751800 = r751791 / r751799;
        double r751801 = r751798 + r751800;
        double r751802 = r751784 ? r751795 : r751801;
        return r751802;
}

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

Original3.4
Target2.0
Herbie2.0
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z 3.0) < 2.4290858547001272e+93

    1. Initial program 4.3

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

    3. Applied associate-/r*2.1

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

    5. Applied *-un-lft-identity2.1

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

    6. Applied times-frac2.2

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

    7. Applied associate-/l*2.5

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

    if 2.4290858547001272e+93 < (* z 3.0)

    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 *-un-lft-identity0.7

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

    4. Applied times-frac0.7

      \[\leadsto \left(x - \color{blue}{\frac{1}{z} \cdot \frac{y}{3}}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le 2.429085854700127248317880955221217421232 \cdot 10^{93}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 
(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))))