Average Error: 12.0 → 2.2
Time: 3.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.54363164202423776 \cdot 10^{-164} \lor \neg \left(z \le 1.03870846195001497 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z} + x \cdot \left(-\frac{z}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + x \cdot \left(-z\right)}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.54363164202423776 \cdot 10^{-164} \lor \neg \left(z \le 1.03870846195001497 \cdot 10^{-26}\right):\\
\;\;\;\;x \cdot \frac{y}{t - z} + x \cdot \left(-\frac{z}{t - z}\right)\\

\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 r592980 = x;
        double r592981 = y;
        double r592982 = z;
        double r592983 = r592981 - r592982;
        double r592984 = r592980 * r592983;
        double r592985 = t;
        double r592986 = r592985 - r592982;
        double r592987 = r592984 / r592986;
        return r592987;
}
↓
double f(double x, double y, double z, double t) {
        double r592988 = z;
        double r592989 = -2.5436316420242378e-164;
        bool r592990 = r592988 <= r592989;
        double r592991 = 1.038708461950015e-26;
        bool r592992 = r592988 <= r592991;
        double r592993 = !r592992;
        bool r592994 = r592990 || r592993;
        double r592995 = x;
        double r592996 = y;
        double r592997 = t;
        double r592998 = r592997 - r592988;
        double r592999 = r592996 / r592998;
        double r593000 = r592995 * r592999;
        double r593001 = r592988 / r592998;
        double r593002 = -r593001;
        double r593003 = r592995 * r593002;
        double r593004 = r593000 + r593003;
        double r593005 = r592995 * r592996;
        double r593006 = -r592988;
        double r593007 = r592995 * r593006;
        double r593008 = r593005 + r593007;
        double r593009 = r593008 / r592998;
        double r593010 = r592994 ? r593004 : r593009;
        return r593010;
}

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

Original12.0
Target2.2
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.5436316420242378e-164 or 1.038708461950015e-26 < z

    1. Initial program 15.1

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

    3. Applied *-un-lft-identity15.1

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

    7. Applied div-sub0.6

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

    9. Applied sub-neg0.6

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

    10. Applied distribute-lft-in0.6

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

    if -2.5436316420242378e-164 < z < 1.038708461950015e-26

    1. Initial program 5.5

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

    3. Applied sub-neg5.5

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

    4. Applied distribute-lft-in5.5

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.54363164202423776 \cdot 10^{-164} \lor \neg \left(z \le 1.03870846195001497 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z} + x \cdot \left(-\frac{z}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + x \cdot \left(-z\right)}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(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)))