Average Error: 2.1 → 1.6
Time: 17.1s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.554277062255470137394898281085509956894 \cdot 10^{-90}:\\ \;\;\;\;\frac{\frac{z - t}{y}}{\frac{1}{x}} + t\\ \mathbf{elif}\;y \le 5.254045475746620239720312111798513775031 \cdot 10^{-51}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.554277062255470137394898281085509956894 \cdot 10^{-90}:\\
\;\;\;\;\frac{\frac{z - t}{y}}{\frac{1}{x}} + t\\

\mathbf{elif}\;y \le 5.254045475746620239720312111798513775031 \cdot 10^{-51}:\\
\;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\

\end{array}
double f(double x, double y, double z, double t) {
        double r302880 = x;
        double r302881 = y;
        double r302882 = r302880 / r302881;
        double r302883 = z;
        double r302884 = t;
        double r302885 = r302883 - r302884;
        double r302886 = r302882 * r302885;
        double r302887 = r302886 + r302884;
        return r302887;
}
↓
double f(double x, double y, double z, double t) {
        double r302888 = y;
        double r302889 = -3.55427706225547e-90;
        bool r302890 = r302888 <= r302889;
        double r302891 = z;
        double r302892 = t;
        double r302893 = r302891 - r302892;
        double r302894 = r302893 / r302888;
        double r302895 = 1.0;
        double r302896 = x;
        double r302897 = r302895 / r302896;
        double r302898 = r302894 / r302897;
        double r302899 = r302898 + r302892;
        double r302900 = 5.25404547574662e-51;
        bool r302901 = r302888 <= r302900;
        double r302902 = r302896 * r302893;
        double r302903 = r302902 / r302888;
        double r302904 = r302903 + r302892;
        double r302905 = r302896 * r302894;
        double r302906 = r302905 + r302892;
        double r302907 = r302901 ? r302904 : r302906;
        double r302908 = r302890 ? r302899 : r302907;
        return r302908;
}

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

Original2.1
Target2.2
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -3.55427706225547e-90

    1. Initial program 1.2

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

    3. Applied *-un-lft-identity1.2

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

    4. Applied *-un-lft-identity1.2

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

    5. Applied times-frac1.2

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

    6. Applied associate-*l*1.2

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

    7. Simplified1.2

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

    9. Applied div-inv1.2

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

    10. Applied associate-/r*1.7

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

    if -3.55427706225547e-90 < y < 5.25404547574662e-51

    1. Initial program 5.0

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

    3. Applied associate-*l/2.0

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

    if 5.25404547574662e-51 < y

    1. Initial program 1.0

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

    3. Applied div-inv1.0

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

    4. Applied associate-*l*1.1

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

    5. Simplified1.1

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.554277062255470137394898281085509956894 \cdot 10^{-90}:\\ \;\;\;\;\frac{\frac{z - t}{y}}{\frac{1}{x}} + t\\ \mathbf{elif}\;y \le 5.254045475746620239720312111798513775031 \cdot 10^{-51}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(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))