Average Error: 6.4 → 2.4
Time: 10.0s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{1}{x} \cdot \frac{z}{y}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -1.121666526734702928844683807180631310871 \cdot 10^{-307}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -0.0:\\ \;\;\;\;\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\
\;\;\;\;\frac{1}{\frac{1}{x} \cdot \frac{z}{y}}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \le -1.121666526734702928844683807180631310871 \cdot 10^{-307}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \le -0.0:\\
\;\;\;\;\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r47420093 = x;
        double r47420094 = y;
        double r47420095 = r47420093 * r47420094;
        double r47420096 = z;
        double r47420097 = r47420095 / r47420096;
        return r47420097;
}
↓
double f(double x, double y, double z) {
        double r47420098 = x;
        double r47420099 = y;
        double r47420100 = r47420098 * r47420099;
        double r47420101 = z;
        double r47420102 = r47420100 / r47420101;
        double r47420103 = -inf.0;
        bool r47420104 = r47420102 <= r47420103;
        double r47420105 = 1.0;
        double r47420106 = r47420105 / r47420098;
        double r47420107 = r47420101 / r47420099;
        double r47420108 = r47420106 * r47420107;
        double r47420109 = r47420105 / r47420108;
        double r47420110 = -1.121666526734703e-307;
        bool r47420111 = r47420102 <= r47420110;
        double r47420112 = -0.0;
        bool r47420113 = r47420102 <= r47420112;
        double r47420114 = cbrt(r47420101);
        double r47420115 = r47420114 * r47420114;
        double r47420116 = r47420098 / r47420115;
        double r47420117 = r47420099 / r47420114;
        double r47420118 = r47420116 * r47420117;
        double r47420119 = r47420113 ? r47420118 : r47420102;
        double r47420120 = r47420111 ? r47420102 : r47420119;
        double r47420121 = r47420104 ? r47420109 : r47420120;
        return r47420121;
}

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

Original6.4
Target6.5
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x y) z) < -inf.0

    1. Initial program 64.0

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

    3. Applied clear-num64.0

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

    5. Applied *-un-lft-identity64.0

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

    6. Applied times-frac0.4

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

    if -inf.0 < (/ (* x y) z) < -1.121666526734703e-307 or -0.0 < (/ (* x y) z)

    1. Initial program 3.1

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

    if -1.121666526734703e-307 < (/ (* x y) z) < -0.0

    1. Initial program 9.9

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

    3. Applied add-cube-cbrt9.9

      \[\leadsto \frac{x \cdot y}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    4. Applied times-frac0.5

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{1}{x} \cdot \frac{z}{y}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -1.121666526734702928844683807180631310871 \cdot 10^{-307}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -0.0:\\ \;\;\;\;\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(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))