Average Error: 11.6 → 2.2
Time: 8.0s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.5433744152148751 \cdot 10^{-69} \lor \neg \left(z \le 1.20407222144680094 \cdot 10^{-212}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + \left(-z\right) \cdot x}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.5433744152148751 \cdot 10^{-69} \lor \neg \left(z \le 1.20407222144680094 \cdot 10^{-212}\right):\\
\;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r770902 = x;
        double r770903 = y;
        double r770904 = z;
        double r770905 = r770903 - r770904;
        double r770906 = r770902 * r770905;
        double r770907 = t;
        double r770908 = r770907 - r770904;
        double r770909 = r770906 / r770908;
        return r770909;
}
↓
double f(double x, double y, double z, double t) {
        double r770910 = z;
        double r770911 = -3.543374415214875e-69;
        bool r770912 = r770910 <= r770911;
        double r770913 = 1.204072221446801e-212;
        bool r770914 = r770910 <= r770913;
        double r770915 = !r770914;
        bool r770916 = r770912 || r770915;
        double r770917 = x;
        double r770918 = t;
        double r770919 = r770918 - r770910;
        double r770920 = y;
        double r770921 = r770920 - r770910;
        double r770922 = r770919 / r770921;
        double r770923 = r770917 / r770922;
        double r770924 = r770920 * r770917;
        double r770925 = -r770910;
        double r770926 = r770925 * r770917;
        double r770927 = r770924 + r770926;
        double r770928 = r770927 / r770919;
        double r770929 = r770916 ? r770923 : r770928;
        return r770929;
}

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

Original11.6
Target2.0
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.543374415214875e-69 or 1.204072221446801e-212 < z

    1. Initial program 13.4

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

    3. Applied associate-/l*1.0

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

    if -3.543374415214875e-69 < z < 1.204072221446801e-212

    1. Initial program 5.9

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

    3. Applied sub-neg5.9

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

    4. Applied distribute-lft-in5.9

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

    5. Simplified5.9

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

    6. Simplified5.9

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.5433744152148751 \cdot 10^{-69} \lor \neg \left(z \le 1.20407222144680094 \cdot 10^{-212}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + \left(-z\right) \cdot x}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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)))