Average Error: 11.9 → 2.0
Time: 4.2s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -8.05105609781592315 \cdot 10^{-223} \lor \neg \left(z \le 1.34650257932233616 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -8.05105609781592315 \cdot 10^{-223} \lor \neg \left(z \le 1.34650257932233616 \cdot 10^{-105}\right):\\
\;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r607851 = x;
        double r607852 = y;
        double r607853 = z;
        double r607854 = r607852 - r607853;
        double r607855 = r607851 * r607854;
        double r607856 = t;
        double r607857 = r607856 - r607853;
        double r607858 = r607855 / r607857;
        return r607858;
}
↓
double f(double x, double y, double z, double t) {
        double r607859 = z;
        double r607860 = -8.051056097815923e-223;
        bool r607861 = r607859 <= r607860;
        double r607862 = 1.3465025793223362e-105;
        bool r607863 = r607859 <= r607862;
        double r607864 = !r607863;
        bool r607865 = r607861 || r607864;
        double r607866 = x;
        double r607867 = t;
        double r607868 = r607867 - r607859;
        double r607869 = y;
        double r607870 = r607869 - r607859;
        double r607871 = r607868 / r607870;
        double r607872 = r607866 / r607871;
        double r607873 = r607866 * r607870;
        double r607874 = r607873 / r607868;
        double r607875 = r607865 ? r607872 : r607874;
        return r607875;
}

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
Herbie2.0
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -8.051056097815923e-223 or 1.3465025793223362e-105 < z

    1. Initial program 13.8

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

    3. Applied associate-/l*1.1

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

    if -8.051056097815923e-223 < z < 1.3465025793223362e-105

    1. Initial program 5.1

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -8.05105609781592315 \cdot 10^{-223} \lor \neg \left(z \le 1.34650257932233616 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 +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)))