Average Error: 11.6 → 2.2
Time: 8.5s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.5433744152148751 \cdot 10^{-69} \lor \neg \left(z \le 1.20407222144680094 \cdot 10^{-212}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + x \cdot \left(-z\right)}{t - z}\\ \end{array}\]
\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{x \cdot y + x \cdot \left(-z\right)}{t - z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r583687 = x;
        double r583688 = y;
        double r583689 = z;
        double r583690 = r583688 - r583689;
        double r583691 = r583687 * r583690;
        double r583692 = t;
        double r583693 = r583692 - r583689;
        double r583694 = r583691 / r583693;
        return r583694;
}
↓
double f(double x, double y, double z, double t) {
        double r583695 = z;
        double r583696 = -3.543374415214875e-69;
        bool r583697 = r583695 <= r583696;
        double r583698 = 1.204072221446801e-212;
        bool r583699 = r583695 <= r583698;
        double r583700 = !r583699;
        bool r583701 = r583697 || r583700;
        double r583702 = x;
        double r583703 = t;
        double r583704 = r583703 - r583695;
        double r583705 = y;
        double r583706 = r583705 - r583695;
        double r583707 = r583704 / r583706;
        double r583708 = r583702 / r583707;
        double r583709 = r583702 * r583705;
        double r583710 = -r583695;
        double r583711 = r583702 * r583710;
        double r583712 = r583709 + r583711;
        double r583713 = r583712 / r583704;
        double r583714 = r583701 ? r583708 : r583713;
        return r583714;
}

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

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

  4. Final simplification2.2

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

Reproduce

herbie shell --seed 2020046 +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)))