Average Error: 6.2 → 0.4
Time: 15.3s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y = -\infty:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -9.822128397102382416352944524673235566637 \cdot 10^{-148}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 2.043259034829907291655254600884174757159 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 3.183191360702753125443234015952073139728 \cdot 10^{226}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y = -\infty:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le -9.822128397102382416352944524673235566637 \cdot 10^{-148}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 2.043259034829907291655254600884174757159 \cdot 10^{-242}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le 3.183191360702753125443234015952073139728 \cdot 10^{226}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\end{array}
double f(double x, double y, double z) {
        double r514871 = x;
        double r514872 = y;
        double r514873 = r514871 * r514872;
        double r514874 = z;
        double r514875 = r514873 / r514874;
        return r514875;
}
↓
double f(double x, double y, double z) {
        double r514876 = x;
        double r514877 = y;
        double r514878 = r514876 * r514877;
        double r514879 = -inf.0;
        bool r514880 = r514878 <= r514879;
        double r514881 = z;
        double r514882 = r514877 / r514881;
        double r514883 = r514876 * r514882;
        double r514884 = -9.822128397102382e-148;
        bool r514885 = r514878 <= r514884;
        double r514886 = r514878 / r514881;
        double r514887 = 2.0432590348299073e-242;
        bool r514888 = r514878 <= r514887;
        double r514889 = 3.183191360702753e+226;
        bool r514890 = r514878 <= r514889;
        double r514891 = r514881 / r514877;
        double r514892 = r514876 / r514891;
        double r514893 = r514890 ? r514886 : r514892;
        double r514894 = r514888 ? r514883 : r514893;
        double r514895 = r514885 ? r514886 : r514894;
        double r514896 = r514880 ? r514883 : r514895;
        return r514896;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.2
Target6.3
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -inf.0 or -9.822128397102382e-148 < (* x y) < 2.0432590348299073e-242

    1. Initial program 14.3

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

    3. Applied *-un-lft-identity14.3

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

    if -inf.0 < (* x y) < -9.822128397102382e-148 or 2.0432590348299073e-242 < (* x y) < 3.183191360702753e+226

    1. Initial program 0.2

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

    if 3.183191360702753e+226 < (* x y)

    1. Initial program 32.6

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

    3. Applied associate-/l*1.1

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y = -\infty:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -9.822128397102382416352944524673235566637 \cdot 10^{-148}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 2.043259034829907291655254600884174757159 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 3.183191360702753125443234015952073139728 \cdot 10^{226}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.70421306606504721e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))