Average Error: 11.9 → 2.3
Time: 3.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.78095534954889683 \cdot 10^{-116} \lor \neg \left(z \le 7.1593596549390092 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.78095534954889683 \cdot 10^{-116} \lor \neg \left(z \le 7.1593596549390092 \cdot 10^{-78}\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 r679316 = x;
        double r679317 = y;
        double r679318 = z;
        double r679319 = r679317 - r679318;
        double r679320 = r679316 * r679319;
        double r679321 = t;
        double r679322 = r679321 - r679318;
        double r679323 = r679320 / r679322;
        return r679323;
}
↓
double f(double x, double y, double z, double t) {
        double r679324 = z;
        double r679325 = -5.780955349548897e-116;
        bool r679326 = r679324 <= r679325;
        double r679327 = 7.159359654939009e-78;
        bool r679328 = r679324 <= r679327;
        double r679329 = !r679328;
        bool r679330 = r679326 || r679329;
        double r679331 = x;
        double r679332 = y;
        double r679333 = r679332 - r679324;
        double r679334 = t;
        double r679335 = r679334 - r679324;
        double r679336 = r679333 / r679335;
        double r679337 = r679331 * r679336;
        double r679338 = r679331 / r679335;
        double r679339 = r679338 * r679333;
        double r679340 = r679330 ? r679337 : r679339;
        return r679340;
}

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

Original11.9
Target2.2
Herbie2.3
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.780955349548897e-116 or 7.159359654939009e-78 < z

    1. Initial program 14.6

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

    3. Applied *-un-lft-identity14.6

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

    4. Applied times-frac0.5

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

    5. Simplified0.5

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

    if -5.780955349548897e-116 < z < 7.159359654939009e-78

    1. Initial program 6.0

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

    3. Applied associate-/l*5.9

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

    5. Applied associate-/r/6.1

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.78095534954889683 \cdot 10^{-116} \lor \neg \left(z \le 7.1593596549390092 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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)))