Average Error: 6.2 → 0.5
Time: 24.5s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -1.871003352164138983509669622339238961491 \cdot 10^{282}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -9.609520285206617620294914143781194869795 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.717842953697809163237341802420612798171 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 3.388277152440999464105996490605589103728 \cdot 10^{143}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -1.871003352164138983509669622339238961491 \cdot 10^{282}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le -9.609520285206617620294914143781194869795 \cdot 10^{-248}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 1.717842953697809163237341802420612798171 \cdot 10^{-196}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;x \cdot y \le 3.388277152440999464105996490605589103728 \cdot 10^{143}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r35715872 = x;
        double r35715873 = y;
        double r35715874 = r35715872 * r35715873;
        double r35715875 = z;
        double r35715876 = r35715874 / r35715875;
        return r35715876;
}
↓
double f(double x, double y, double z) {
        double r35715877 = x;
        double r35715878 = y;
        double r35715879 = r35715877 * r35715878;
        double r35715880 = -1.871003352164139e+282;
        bool r35715881 = r35715879 <= r35715880;
        double r35715882 = z;
        double r35715883 = r35715882 / r35715878;
        double r35715884 = r35715877 / r35715883;
        double r35715885 = -9.609520285206618e-248;
        bool r35715886 = r35715879 <= r35715885;
        double r35715887 = r35715879 / r35715882;
        double r35715888 = 1.7178429536978092e-196;
        bool r35715889 = r35715879 <= r35715888;
        double r35715890 = r35715878 / r35715882;
        double r35715891 = r35715890 * r35715877;
        double r35715892 = 3.3882771524409995e+143;
        bool r35715893 = r35715879 <= r35715892;
        double r35715894 = r35715893 ? r35715887 : r35715891;
        double r35715895 = r35715889 ? r35715891 : r35715894;
        double r35715896 = r35715886 ? r35715887 : r35715895;
        double r35715897 = r35715881 ? r35715884 : r35715896;
        return r35715897;
}

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
Target6.4
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -1.871003352164139e+282

    1. Initial program 54.8

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

    3. Applied associate-/l*0.3

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

    if -1.871003352164139e+282 < (* x y) < -9.609520285206618e-248 or 1.7178429536978092e-196 < (* x y) < 3.3882771524409995e+143

    1. Initial program 0.2

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

    if -9.609520285206618e-248 < (* x y) < 1.7178429536978092e-196 or 3.3882771524409995e+143 < (* x y)

    1. Initial program 13.3

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

    3. Applied *-un-lft-identity13.3

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

    4. Applied times-frac1.1

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

    5. Simplified1.1

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -1.871003352164138983509669622339238961491 \cdot 10^{282}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -9.609520285206617620294914143781194869795 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.717842953697809163237341802420612798171 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 3.388277152440999464105996490605589103728 \cdot 10^{143}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))