Average Error: 11.1 → 1.3
Time: 11.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 3.016949263831516 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 5.367760633924734 \cdot 10^{+261}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 3.016949263831516 \cdot 10^{-301}:\\
\;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 5.367760633924734 \cdot 10^{+261}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r29774869 = x;
        double r29774870 = y;
        double r29774871 = z;
        double r29774872 = r29774870 - r29774871;
        double r29774873 = r29774869 * r29774872;
        double r29774874 = t;
        double r29774875 = r29774874 - r29774871;
        double r29774876 = r29774873 / r29774875;
        return r29774876;
}
↓
double f(double x, double y, double z, double t) {
        double r29774877 = y;
        double r29774878 = z;
        double r29774879 = r29774877 - r29774878;
        double r29774880 = x;
        double r29774881 = r29774879 * r29774880;
        double r29774882 = t;
        double r29774883 = r29774882 - r29774878;
        double r29774884 = r29774881 / r29774883;
        double r29774885 = 3.016949263831516e-301;
        bool r29774886 = r29774884 <= r29774885;
        double r29774887 = r29774883 / r29774879;
        double r29774888 = r29774880 / r29774887;
        double r29774889 = 5.367760633924734e+261;
        bool r29774890 = r29774884 <= r29774889;
        double r29774891 = r29774879 / r29774883;
        double r29774892 = r29774880 * r29774891;
        double r29774893 = r29774890 ? r29774884 : r29774892;
        double r29774894 = r29774886 ? r29774888 : r29774893;
        return r29774894;
}

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

Original11.1
Target2.1
Herbie1.3
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) (- t z)) < 3.016949263831516e-301

    1. Initial program 10.9

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

    3. Applied associate-/l*1.9

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}}\]

    if 3.016949263831516e-301 < (/ (* x (- y z)) (- t z)) < 5.367760633924734e+261

    1. Initial program 0.3

      \[\frac{x \cdot \left(y - z\right)}{t - z}\]

    if 5.367760633924734e+261 < (/ (* x (- y z)) (- t z))

    1. Initial program 53.2

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

    3. Applied *-un-lft-identity53.2

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

    4. Applied times-frac1.4

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{t - z}}\]

    5. Simplified1.4

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 3.016949263831516 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 5.367760633924734 \cdot 10^{+261}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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