Average Error: 11.9 → 2.3
Time: 4.6s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.78095534954889683 \cdot 10^{-116} \lor \neg \left(z \le 7.1593596549390092 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.78095534954889683 \cdot 10^{-116} \lor \neg \left(z \le 7.1593596549390092 \cdot 10^{-78}\right):\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r829895 = x;
        double r829896 = y;
        double r829897 = z;
        double r829898 = r829896 - r829897;
        double r829899 = r829895 * r829898;
        double r829900 = t;
        double r829901 = r829900 - r829897;
        double r829902 = r829899 / r829901;
        return r829902;
}
↓
double f(double x, double y, double z, double t) {
        double r829903 = z;
        double r829904 = -5.780955349548897e-116;
        bool r829905 = r829903 <= r829904;
        double r829906 = 7.159359654939009e-78;
        bool r829907 = r829903 <= r829906;
        double r829908 = !r829907;
        bool r829909 = r829905 || r829908;
        double r829910 = x;
        double r829911 = y;
        double r829912 = r829911 - r829903;
        double r829913 = t;
        double r829914 = r829913 - r829903;
        double r829915 = r829912 / r829914;
        double r829916 = r829910 * r829915;
        double r829917 = r829910 / r829914;
        double r829918 = r829912 * r829917;
        double r829919 = r829909 ? r829916 : r829918;
        return r829919;
}

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

Original11.9
Target2.2
Herbie2.3
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.780955349548897e-116 or 7.159359654939009e-78 < z

    1. Initial program 14.6

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

    3. Applied *-un-lft-identity14.6

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

    4. Applied times-frac0.5

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

    5. Simplified0.5

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

    if -5.780955349548897e-116 < z < 7.159359654939009e-78

    1. Initial program 6.0

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

    3. Applied associate-/l*5.9

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}}\]
    4. Using strategy rm

    5. Applied div-sub5.9

      \[\leadsto \frac{x}{\color{blue}{\frac{t}{y - z} - \frac{z}{y - z}}}\]
    6. Using strategy rm

    7. Applied div-inv5.9

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

    8. Applied div-inv5.9

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

    9. Applied distribute-rgt-out--5.9

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

    10. Applied *-un-lft-identity5.9

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

    11. Applied times-frac6.1

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

    12. Simplified6.1

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.78095534954889683 \cdot 10^{-116} \lor \neg \left(z \le 7.1593596549390092 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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