Average Error: 11.4 → 1.5
Time: 4.1s
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 r539585 = x;
        double r539586 = y;
        double r539587 = z;
        double r539588 = r539586 - r539587;
        double r539589 = r539585 * r539588;
        double r539590 = t;
        double r539591 = r539590 - r539587;
        double r539592 = r539589 / r539591;
        return r539592;
}
↓
double f(double x, double y, double z, double t) {
        double r539593 = x;
        double r539594 = y;
        double r539595 = z;
        double r539596 = r539594 - r539595;
        double r539597 = r539593 * r539596;
        double r539598 = t;
        double r539599 = r539598 - r539595;
        double r539600 = r539597 / r539599;
        double r539601 = -1.353657953588875e+306;
        bool r539602 = r539600 <= r539601;
        double r539603 = r539599 / r539596;
        double r539604 = r539593 / r539603;
        double r539605 = -3.377554219823078e-299;
        bool r539606 = r539600 <= r539605;
        double r539607 = r539596 / r539599;
        double r539608 = r539593 * r539607;
        double r539609 = r539606 ? r539600 : r539608;
        double r539610 = r539602 ? r539604 : r539609;
        return r539610;
}

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)))