Average Error: 11.5 → 2.0
Time: 17.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.521150424857788861649339444118342642553 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \mathbf{elif}\;z \le 4.55133529175129052669496720638249750795 \cdot 10^{-204}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.521150424857788861649339444118342642553 \cdot 10^{-190}:\\
\;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\

\mathbf{elif}\;z \le 4.55133529175129052669496720638249750795 \cdot 10^{-204}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r24950752 = x;
        double r24950753 = y;
        double r24950754 = z;
        double r24950755 = r24950753 - r24950754;
        double r24950756 = r24950752 * r24950755;
        double r24950757 = t;
        double r24950758 = r24950757 - r24950754;
        double r24950759 = r24950756 / r24950758;
        return r24950759;
}
↓
double f(double x, double y, double z, double t) {
        double r24950760 = z;
        double r24950761 = -1.5211504248577889e-190;
        bool r24950762 = r24950760 <= r24950761;
        double r24950763 = x;
        double r24950764 = t;
        double r24950765 = y;
        double r24950766 = r24950765 - r24950760;
        double r24950767 = r24950764 / r24950766;
        double r24950768 = r24950760 / r24950766;
        double r24950769 = r24950767 - r24950768;
        double r24950770 = r24950763 / r24950769;
        double r24950771 = 4.5513352917512905e-204;
        bool r24950772 = r24950760 <= r24950771;
        double r24950773 = r24950763 * r24950766;
        double r24950774 = r24950764 - r24950760;
        double r24950775 = r24950773 / r24950774;
        double r24950776 = r24950772 ? r24950775 : r24950770;
        double r24950777 = r24950762 ? r24950770 : r24950776;
        return r24950777;
}

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

Original11.5
Target2.0
Herbie2.0
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.5211504248577889e-190 or 4.5513352917512905e-204 < z

    1. Initial program 12.6

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

    3. Applied associate-/l*1.3

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

    5. Applied div-sub1.3

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

    if -1.5211504248577889e-190 < z < 4.5513352917512905e-204

    1. Initial program 5.8

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.521150424857788861649339444118342642553 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \mathbf{elif}\;z \le 4.55133529175129052669496720638249750795 \cdot 10^{-204}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

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

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