Average Error: 6.3 → 0.8
Time: 2.2s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -7.725807749934587 \cdot 10^{96}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;x \cdot y \le -3.0807367441454416 \cdot 10^{-282}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le -0.0:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 5.31151602867187701 \cdot 10^{255}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{\frac{x}{\frac{z}{y}}}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -7.725807749934587 \cdot 10^{96}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

\mathbf{elif}\;x \cdot y \le -3.0807367441454416 \cdot 10^{-282}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le -0.0:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le 5.31151602867187701 \cdot 10^{255}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{1}{\frac{x}{\frac{z}{y}}}}\\

\end{array}
double f(double x, double y, double z) {
        double r949885 = x;
        double r949886 = y;
        double r949887 = r949885 * r949886;
        double r949888 = z;
        double r949889 = r949887 / r949888;
        return r949889;
}
↓
double f(double x, double y, double z) {
        double r949890 = x;
        double r949891 = y;
        double r949892 = r949890 * r949891;
        double r949893 = -7.725807749934587e+96;
        bool r949894 = r949892 <= r949893;
        double r949895 = z;
        double r949896 = r949890 / r949895;
        double r949897 = r949896 * r949891;
        double r949898 = -3.0807367441454416e-282;
        bool r949899 = r949892 <= r949898;
        double r949900 = r949892 / r949895;
        double r949901 = -0.0;
        bool r949902 = r949892 <= r949901;
        double r949903 = r949891 / r949895;
        double r949904 = r949890 * r949903;
        double r949905 = 5.311516028671877e+255;
        bool r949906 = r949892 <= r949905;
        double r949907 = 1.0;
        double r949908 = r949895 / r949891;
        double r949909 = r949890 / r949908;
        double r949910 = r949907 / r949909;
        double r949911 = r949907 / r949910;
        double r949912 = r949906 ? r949900 : r949911;
        double r949913 = r949902 ? r949904 : r949912;
        double r949914 = r949899 ? r949900 : r949913;
        double r949915 = r949894 ? r949897 : r949914;
        return r949915;
}

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

Original6.3
Target6.4
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (* x y) < -7.725807749934587e+96

    1. Initial program 14.6

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

    3. Applied associate-/l*3.3

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
    4. Using strategy rm

    5. Applied associate-/r/4.1

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

    if -7.725807749934587e+96 < (* x y) < -3.0807367441454416e-282 or -0.0 < (* x y) < 5.311516028671877e+255

    1. Initial program 0.4

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

    if -3.0807367441454416e-282 < (* x y) < -0.0

    1. Initial program 17.6

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

    3. Applied *-un-lft-identity17.6

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    if 5.311516028671877e+255 < (* x y)

    1. Initial program 40.0

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

    3. Applied associate-/l*0.3

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
    4. Using strategy rm

    5. Applied clear-num0.3

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{z}{y}}{x}}}\]
    6. Using strategy rm

    7. Applied clear-num0.4

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{x}{\frac{z}{y}}}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -7.725807749934587 \cdot 10^{96}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;x \cdot y \le -3.0807367441454416 \cdot 10^{-282}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le -0.0:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 5.31151602867187701 \cdot 10^{255}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{\frac{x}{\frac{z}{y}}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +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 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))