Average Error: 11.9 → 2.1
Time: 3.0s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.29927142667181471 \cdot 10^{-59} \lor \neg \left(z \le -8.2043700554885046 \cdot 10^{-288}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.29927142667181471 \cdot 10^{-59} \lor \neg \left(z \le -8.2043700554885046 \cdot 10^{-288}\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 r588905 = x;
        double r588906 = y;
        double r588907 = z;
        double r588908 = r588906 - r588907;
        double r588909 = r588905 * r588908;
        double r588910 = t;
        double r588911 = r588910 - r588907;
        double r588912 = r588909 / r588911;
        return r588912;
}
↓
double f(double x, double y, double z, double t) {
        double r588913 = z;
        double r588914 = -3.2992714266718147e-59;
        bool r588915 = r588913 <= r588914;
        double r588916 = -8.204370055488505e-288;
        bool r588917 = r588913 <= r588916;
        double r588918 = !r588917;
        bool r588919 = r588915 || r588918;
        double r588920 = x;
        double r588921 = t;
        double r588922 = r588921 - r588913;
        double r588923 = y;
        double r588924 = r588923 - r588913;
        double r588925 = r588922 / r588924;
        double r588926 = r588920 / r588925;
        double r588927 = r588920 * r588924;
        double r588928 = r588927 / r588922;
        double r588929 = r588919 ? r588926 : r588928;
        return r588929;
}

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
Herbie2.1
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.2992714266718147e-59 or -8.204370055488505e-288 < z

    1. Initial program 13.3

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

    3. Applied associate-/l*1.6

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

    if -3.2992714266718147e-59 < z < -8.204370055488505e-288

    1. Initial program 4.7

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.29927142667181471 \cdot 10^{-59} \lor \neg \left(z \le -8.2043700554885046 \cdot 10^{-288}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 +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)))