Average Error: 11.6 → 2.1
Time: 10.6s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5.089780698062090774608904448505777443405 \cdot 10^{-199} \lor \neg \left(x \le 118151073605098128543842304\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t - z} \cdot \left(x \cdot \left(y - z\right)\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -5.089780698062090774608904448505777443405 \cdot 10^{-199} \lor \neg \left(x \le 118151073605098128543842304\right):\\
\;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{t - z} \cdot \left(x \cdot \left(y - z\right)\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r466245 = x;
        double r466246 = y;
        double r466247 = z;
        double r466248 = r466246 - r466247;
        double r466249 = r466245 * r466248;
        double r466250 = t;
        double r466251 = r466250 - r466247;
        double r466252 = r466249 / r466251;
        return r466252;
}
↓
double f(double x, double y, double z, double t) {
        double r466253 = x;
        double r466254 = -5.089780698062091e-199;
        bool r466255 = r466253 <= r466254;
        double r466256 = 1.1815107360509813e+26;
        bool r466257 = r466253 <= r466256;
        double r466258 = !r466257;
        bool r466259 = r466255 || r466258;
        double r466260 = t;
        double r466261 = z;
        double r466262 = r466260 - r466261;
        double r466263 = y;
        double r466264 = r466263 - r466261;
        double r466265 = r466262 / r466264;
        double r466266 = r466253 / r466265;
        double r466267 = 1.0;
        double r466268 = r466267 / r466262;
        double r466269 = r466253 * r466264;
        double r466270 = r466268 * r466269;
        double r466271 = r466259 ? r466266 : r466270;
        return r466271;
}

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

Original11.6
Target2.2
Herbie2.1
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -5.089780698062091e-199 or 1.1815107360509813e+26 < x

    1. Initial program 17.7

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

    3. Applied associate-/l*2.1

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

    if -5.089780698062091e-199 < x < 1.1815107360509813e+26

    1. Initial program 2.0

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

    3. Applied clear-num2.4

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

    5. Applied div-inv2.8

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

    6. Applied add-cube-cbrt2.8

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\left(t - z\right) \cdot \frac{1}{x \cdot \left(y - z\right)}}\]

    7. Applied times-frac2.5

      \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{t - z} \cdot \frac{\sqrt[3]{1}}{\frac{1}{x \cdot \left(y - z\right)}}}\]

    8. Simplified2.5

      \[\leadsto \color{blue}{\frac{1}{t - z}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{x \cdot \left(y - z\right)}}\]

    9. Simplified2.1

      \[\leadsto \frac{1}{t - z} \cdot \color{blue}{\left(x \cdot \left(y - z\right)\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.089780698062090774608904448505777443405 \cdot 10^{-199} \lor \neg \left(x \le 118151073605098128543842304\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t - z} \cdot \left(x \cdot \left(y - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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)))