Average Error: 2.0 → 1.5
Time: 13.6s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.4631969570436788 \cdot 10^{58} \lor \neg \left(y \le 3.1486740368353013 \cdot 10^{-100}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.4631969570436788 \cdot 10^{58} \lor \neg \left(y \le 3.1486740368353013 \cdot 10^{-100}\right):\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r600908 = x;
        double r600909 = y;
        double r600910 = r600908 / r600909;
        double r600911 = z;
        double r600912 = t;
        double r600913 = r600911 - r600912;
        double r600914 = r600910 * r600913;
        double r600915 = r600914 + r600912;
        return r600915;
}
↓
double f(double x, double y, double z, double t) {
        double r600916 = y;
        double r600917 = -2.4631969570436788e+58;
        bool r600918 = r600916 <= r600917;
        double r600919 = 3.1486740368353013e-100;
        bool r600920 = r600916 <= r600919;
        double r600921 = !r600920;
        bool r600922 = r600918 || r600921;
        double r600923 = x;
        double r600924 = r600923 / r600916;
        double r600925 = z;
        double r600926 = t;
        double r600927 = r600925 - r600926;
        double r600928 = r600924 * r600927;
        double r600929 = r600928 + r600926;
        double r600930 = r600923 * r600927;
        double r600931 = r600930 / r600916;
        double r600932 = r600931 + r600926;
        double r600933 = r600922 ? r600929 : r600932;
        return r600933;
}

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

Original2.0
Target2.3
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.4631969570436788e+58 or 3.1486740368353013e-100 < y

    1. Initial program 1.1

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

    if -2.4631969570436788e+58 < y < 3.1486740368353013e-100

    1. Initial program 3.6

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

    3. Applied associate-*l/2.1

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.4631969570436788 \cdot 10^{58} \lor \neg \left(y \le 3.1486740368353013 \cdot 10^{-100}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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))