Average Error: 11.6 → 2.1
Time: 11.0s
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 r399460 = x;
        double r399461 = y;
        double r399462 = z;
        double r399463 = r399461 - r399462;
        double r399464 = r399460 * r399463;
        double r399465 = t;
        double r399466 = r399465 - r399462;
        double r399467 = r399464 / r399466;
        return r399467;
}
↓
double f(double x, double y, double z, double t) {
        double r399468 = x;
        double r399469 = -5.089780698062091e-199;
        bool r399470 = r399468 <= r399469;
        double r399471 = 1.1815107360509813e+26;
        bool r399472 = r399468 <= r399471;
        double r399473 = !r399472;
        bool r399474 = r399470 || r399473;
        double r399475 = t;
        double r399476 = z;
        double r399477 = r399475 - r399476;
        double r399478 = y;
        double r399479 = r399478 - r399476;
        double r399480 = r399477 / r399479;
        double r399481 = r399468 / r399480;
        double r399482 = 1.0;
        double r399483 = r399482 / r399477;
        double r399484 = r399468 * r399479;
        double r399485 = r399483 * r399484;
        double r399486 = r399474 ? r399481 : r399485;
        return r399486;
}

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)))