Average Error: 2.3 → 2.4
Time: 4.5s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -9.3910125961314414 \cdot 10^{-161} \lor \neg \left(y \le 6.0401320354982989 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \left(\frac{t}{z - y} \cdot \left(x - y\right)\right)\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -9.3910125961314414 \cdot 10^{-161} \lor \neg \left(y \le 6.0401320354982989 \cdot 10^{-75}\right):\\
\;\;\;\;\frac{x - y}{z - y} \cdot t\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \left(\frac{t}{z - y} \cdot \left(x - y\right)\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r425845 = x;
        double r425846 = y;
        double r425847 = r425845 - r425846;
        double r425848 = z;
        double r425849 = r425848 - r425846;
        double r425850 = r425847 / r425849;
        double r425851 = t;
        double r425852 = r425850 * r425851;
        return r425852;
}
↓
double f(double x, double y, double z, double t) {
        double r425853 = y;
        double r425854 = -9.391012596131441e-161;
        bool r425855 = r425853 <= r425854;
        double r425856 = 6.040132035498299e-75;
        bool r425857 = r425853 <= r425856;
        double r425858 = !r425857;
        bool r425859 = r425855 || r425858;
        double r425860 = x;
        double r425861 = r425860 - r425853;
        double r425862 = z;
        double r425863 = r425862 - r425853;
        double r425864 = r425861 / r425863;
        double r425865 = t;
        double r425866 = r425864 * r425865;
        double r425867 = 1.0;
        double r425868 = cbrt(r425867);
        double r425869 = r425868 * r425868;
        double r425870 = r425869 / r425867;
        double r425871 = r425865 / r425863;
        double r425872 = r425871 * r425861;
        double r425873 = r425870 * r425872;
        double r425874 = r425859 ? r425866 : r425873;
        return r425874;
}

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

Original2.3
Target2.3
Herbie2.4
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -9.391012596131441e-161 or 6.040132035498299e-75 < y

    1. Initial program 1.0

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

    if -9.391012596131441e-161 < y < 6.040132035498299e-75

    1. Initial program 5.7

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

    3. Applied clear-num6.1

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

    5. Applied *-un-lft-identity6.1

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

    6. Applied *-un-lft-identity6.1

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

    7. Applied times-frac6.1

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

    8. Applied add-cube-cbrt6.1

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

    9. Applied times-frac6.1

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

    10. Applied associate-*l*6.1

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

    11. Simplified5.7

      \[\leadsto \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}} \cdot \color{blue}{\frac{t}{\frac{z - y}{x - y}}}\]
    12. Using strategy rm

    13. Applied associate-/r/6.2

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -9.3910125961314414 \cdot 10^{-161} \lor \neg \left(y \le 6.0401320354982989 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \left(\frac{t}{z - y} \cdot \left(x - y\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))