Average Error: 11.3 → 2.4
Time: 10.2s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.3901733726023231 \cdot 10^{33} \lor \neg \left(z \le -1.7069294686818465 \cdot 10^{-261}\right):\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.3901733726023231 \cdot 10^{33} \lor \neg \left(z \le -1.7069294686818465 \cdot 10^{-261}\right):\\
\;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r612828 = x;
        double r612829 = y;
        double r612830 = z;
        double r612831 = r612829 - r612830;
        double r612832 = r612828 * r612831;
        double r612833 = t;
        double r612834 = r612833 - r612830;
        double r612835 = r612832 / r612834;
        return r612835;
}
↓
double f(double x, double y, double z, double t) {
        double r612836 = z;
        double r612837 = -1.390173372602323e+33;
        bool r612838 = r612836 <= r612837;
        double r612839 = -1.7069294686818465e-261;
        bool r612840 = r612836 <= r612839;
        double r612841 = !r612840;
        bool r612842 = r612838 || r612841;
        double r612843 = x;
        double r612844 = t;
        double r612845 = y;
        double r612846 = r612845 - r612836;
        double r612847 = r612844 / r612846;
        double r612848 = r612836 / r612846;
        double r612849 = r612847 - r612848;
        double r612850 = r612843 / r612849;
        double r612851 = r612844 - r612836;
        double r612852 = r612843 / r612851;
        double r612853 = r612846 * r612852;
        double r612854 = r612842 ? r612850 : r612853;
        return r612854;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original11.3
Target2.0
Herbie2.4
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.390173372602323e+33 or -1.7069294686818465e-261 < z

    1. Initial program 13.1

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

    3. Applied associate-/l*1.7

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

    5. Applied div-sub1.7

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

    if -1.390173372602323e+33 < z < -1.7069294686818465e-261

    1. Initial program 5.1

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

    3. Applied *-un-lft-identity5.1

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

    4. Applied times-frac3.3

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

    5. Simplified3.3

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

    7. Applied *-un-lft-identity3.3

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

    8. Applied associate-*l*3.3

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

    9. Simplified4.6

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.3901733726023231 \cdot 10^{33} \lor \neg \left(z \le -1.7069294686818465 \cdot 10^{-261}\right):\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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)))