Average Error: 11.7 → 2.2
Time: 11.7s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.153665000670807243610753385014101723958 \cdot 10^{-33} \lor \neg \left(z \le -8.57064563000426938033157202013038804801 \cdot 10^{-270}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.153665000670807243610753385014101723958 \cdot 10^{-33} \lor \neg \left(z \le -8.57064563000426938033157202013038804801 \cdot 10^{-270}\right):\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r435635 = x;
        double r435636 = y;
        double r435637 = z;
        double r435638 = r435636 - r435637;
        double r435639 = r435635 * r435638;
        double r435640 = t;
        double r435641 = r435640 - r435637;
        double r435642 = r435639 / r435641;
        return r435642;
}
↓
double f(double x, double y, double z, double t) {
        double r435643 = z;
        double r435644 = -1.1536650006708072e-33;
        bool r435645 = r435643 <= r435644;
        double r435646 = -8.57064563000427e-270;
        bool r435647 = r435643 <= r435646;
        double r435648 = !r435647;
        bool r435649 = r435645 || r435648;
        double r435650 = x;
        double r435651 = y;
        double r435652 = r435651 - r435643;
        double r435653 = t;
        double r435654 = r435653 - r435643;
        double r435655 = r435652 / r435654;
        double r435656 = r435650 * r435655;
        double r435657 = r435650 / r435654;
        double r435658 = r435657 * r435652;
        double r435659 = r435649 ? r435656 : r435658;
        return r435659;
}

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

Original11.7
Target2.3
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.1536650006708072e-33 or -8.57064563000427e-270 < z

    1. Initial program 13.2

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

    3. Applied *-un-lft-identity13.2

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

    4. Applied times-frac1.7

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

    5. Simplified1.7

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

    if -1.1536650006708072e-33 < z < -8.57064563000427e-270

    1. Initial program 5.3

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

    3. Applied associate-/l*5.2

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

    5. Applied associate-/r/4.5

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.153665000670807243610753385014101723958 \cdot 10^{-33} \lor \neg \left(z \le -8.57064563000426938033157202013038804801 \cdot 10^{-270}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 
(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)))