Average Error: 2.2 → 1.6
Time: 15.1s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.3965576020640518 \cdot 10^{99}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;y \le 1.47008867651433422 \cdot 10^{-30}:\\ \;\;\;\;\left(\frac{x \cdot z}{y} - \frac{t \cdot x}{y}\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.3965576020640518 \cdot 10^{99}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\

\mathbf{elif}\;y \le 1.47008867651433422 \cdot 10^{-30}:\\
\;\;\;\;\left(\frac{x \cdot z}{y} - \frac{t \cdot x}{y}\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r639850 = x;
        double r639851 = y;
        double r639852 = r639850 / r639851;
        double r639853 = z;
        double r639854 = t;
        double r639855 = r639853 - r639854;
        double r639856 = r639852 * r639855;
        double r639857 = r639856 + r639854;
        return r639857;
}
↓
double f(double x, double y, double z, double t) {
        double r639858 = y;
        double r639859 = -2.396557602064052e+99;
        bool r639860 = r639858 <= r639859;
        double r639861 = x;
        double r639862 = z;
        double r639863 = t;
        double r639864 = r639862 - r639863;
        double r639865 = r639864 / r639858;
        double r639866 = r639861 * r639865;
        double r639867 = r639866 + r639863;
        double r639868 = 1.4700886765143342e-30;
        bool r639869 = r639858 <= r639868;
        double r639870 = r639861 * r639862;
        double r639871 = r639870 / r639858;
        double r639872 = r639863 * r639861;
        double r639873 = r639872 / r639858;
        double r639874 = r639871 - r639873;
        double r639875 = r639874 + r639863;
        double r639876 = r639861 / r639858;
        double r639877 = r639876 * r639864;
        double r639878 = r639877 + r639863;
        double r639879 = r639869 ? r639875 : r639878;
        double r639880 = r639860 ? r639867 : r639879;
        return r639880;
}

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

Original2.2
Target2.5
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -2.396557602064052e+99

    1. Initial program 1.4

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

    3. Applied div-inv1.4

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

    4. Applied associate-*l*1.2

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

    5. Simplified1.1

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

    if -2.396557602064052e+99 < y < 1.4700886765143342e-30

    1. Initial program 3.5

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

    3. Applied add-cube-cbrt4.2

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

    4. Applied *-un-lft-identity4.2

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

    5. Applied times-frac4.2

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

    6. Applied associate-*l*2.3

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

    7. Taylor expanded around 0 2.1

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

    if 1.4700886765143342e-30 < y

    1. Initial program 1.1

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.3965576020640518 \cdot 10^{99}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;y \le 1.47008867651433422 \cdot 10^{-30}:\\ \;\;\;\;\left(\frac{x \cdot z}{y} - \frac{t \cdot x}{y}\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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