Average Error: 11.9 → 2.3
Time: 4.2s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.78095534954889683 \cdot 10^{-116} \lor \neg \left(z \le 7.1593596549390092 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]
\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}:\\
\;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r678781 = x;
        double r678782 = y;
        double r678783 = z;
        double r678784 = r678782 - r678783;
        double r678785 = r678781 * r678784;
        double r678786 = t;
        double r678787 = r678786 - r678783;
        double r678788 = r678785 / r678787;
        return r678788;
}
↓
double f(double x, double y, double z, double t) {
        double r678789 = z;
        double r678790 = -5.780955349548897e-116;
        bool r678791 = r678789 <= r678790;
        double r678792 = 7.159359654939009e-78;
        bool r678793 = r678789 <= r678792;
        double r678794 = !r678793;
        bool r678795 = r678791 || r678794;
        double r678796 = x;
        double r678797 = y;
        double r678798 = r678797 - r678789;
        double r678799 = t;
        double r678800 = r678799 - r678789;
        double r678801 = r678798 / r678800;
        double r678802 = r678796 * r678801;
        double r678803 = r678796 / r678800;
        double r678804 = r678803 * r678798;
        double r678805 = r678795 ? r678802 : r678804;
        return r678805;
}

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 associate-/r/6.1

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

  4. Final simplification2.3

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

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)))