Average Error: 11.6 → 2.2
Time: 7.9s
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 r554677 = x;
        double r554678 = y;
        double r554679 = z;
        double r554680 = r554678 - r554679;
        double r554681 = r554677 * r554680;
        double r554682 = t;
        double r554683 = r554682 - r554679;
        double r554684 = r554681 / r554683;
        return r554684;
}
↓
double f(double x, double y, double z, double t) {
        double r554685 = z;
        double r554686 = -3.543374415214875e-69;
        bool r554687 = r554685 <= r554686;
        double r554688 = 1.204072221446801e-212;
        bool r554689 = r554685 <= r554688;
        double r554690 = !r554689;
        bool r554691 = r554687 || r554690;
        double r554692 = x;
        double r554693 = t;
        double r554694 = r554693 - r554685;
        double r554695 = y;
        double r554696 = r554695 - r554685;
        double r554697 = r554694 / r554696;
        double r554698 = r554692 / r554697;
        double r554699 = r554692 * r554695;
        double r554700 = -r554685;
        double r554701 = r554692 * r554700;
        double r554702 = r554699 + r554701;
        double r554703 = r554702 / r554694;
        double r554704 = r554691 ? r554698 : r554703;
        return r554704;
}

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)))