Average Error: 11.4 → 1.5
Time: 11.8s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -1.353657953588875008584498903337160668689 \cdot 10^{306}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -3.37755421982307784760864075070745739156 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -1.353657953588875008584498903337160668689 \cdot 10^{306}:\\
\;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -3.37755421982307784760864075070745739156 \cdot 10^{-299}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r484641 = x;
        double r484642 = y;
        double r484643 = z;
        double r484644 = r484642 - r484643;
        double r484645 = r484641 * r484644;
        double r484646 = t;
        double r484647 = r484646 - r484643;
        double r484648 = r484645 / r484647;
        return r484648;
}
↓
double f(double x, double y, double z, double t) {
        double r484649 = x;
        double r484650 = y;
        double r484651 = z;
        double r484652 = r484650 - r484651;
        double r484653 = r484649 * r484652;
        double r484654 = t;
        double r484655 = r484654 - r484651;
        double r484656 = r484653 / r484655;
        double r484657 = -1.353657953588875e+306;
        bool r484658 = r484656 <= r484657;
        double r484659 = r484655 / r484652;
        double r484660 = r484649 / r484659;
        double r484661 = -3.377554219823078e-299;
        bool r484662 = r484656 <= r484661;
        double r484663 = r484652 / r484655;
        double r484664 = r484649 * r484663;
        double r484665 = r484662 ? r484656 : r484664;
        double r484666 = r484658 ? r484660 : r484665;
        return r484666;
}

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

Original11.4
Target2.3
Herbie1.5
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) (- t z)) < -1.353657953588875e+306

    1. Initial program 63.7

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

    3. Applied associate-/l*0.1

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

    if -1.353657953588875e+306 < (/ (* x (- y z)) (- t z)) < -3.377554219823078e-299

    1. Initial program 0.3

      \[\frac{x \cdot \left(y - z\right)}{t - z}\]

    if -3.377554219823078e-299 < (/ (* x (- y z)) (- t z))

    1. Initial program 11.0

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

    3. Applied *-un-lft-identity11.0

      \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{1 \cdot \left(t - z\right)}}\]

    4. Applied times-frac2.5

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{t - z}}\]

    5. Simplified2.5

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -1.353657953588875008584498903337160668689 \cdot 10^{306}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -3.37755421982307784760864075070745739156 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(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)))