Average Error: 6.5 → 0.7
Time: 2.2s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -2.75403327231568085421125185005337842666 \cdot 10^{-316}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 0.0:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 3.90915317948964794762777056224645120804 \cdot 10^{266}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \le -2.75403327231568085421125185005337842666 \cdot 10^{-316}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\mathbf{elif}\;\frac{x \cdot y}{z} \le 3.90915317948964794762777056224645120804 \cdot 10^{266}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r765211 = x;
        double r765212 = y;
        double r765213 = r765211 * r765212;
        double r765214 = z;
        double r765215 = r765213 / r765214;
        return r765215;
}
↓
double f(double x, double y, double z) {
        double r765216 = x;
        double r765217 = y;
        double r765218 = r765216 * r765217;
        double r765219 = z;
        double r765220 = r765218 / r765219;
        double r765221 = -inf.0;
        bool r765222 = r765220 <= r765221;
        double r765223 = r765219 / r765217;
        double r765224 = r765216 / r765223;
        double r765225 = -2.7540332723157e-316;
        bool r765226 = r765220 <= r765225;
        double r765227 = 0.0;
        bool r765228 = r765220 <= r765227;
        double r765229 = r765217 / r765219;
        double r765230 = r765216 * r765229;
        double r765231 = 3.909153179489648e+266;
        bool r765232 = r765220 <= r765231;
        double r765233 = r765232 ? r765220 : r765230;
        double r765234 = r765228 ? r765230 : r765233;
        double r765235 = r765226 ? r765220 : r765234;
        double r765236 = r765222 ? r765224 : r765235;
        return r765236;
}

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

Original6.5
Target6.5
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

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 associate-/l*0.2

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

    if -inf.0 < (/ (* x y) z) < -2.7540332723157e-316 or 0.0 < (/ (* x y) z) < 3.909153179489648e+266

    1. Initial program 2.2

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

    3. Applied add-cube-cbrt3.2

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

    4. Applied times-frac6.4

      \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}}}\]
    5. Using strategy rm

    6. Applied frac-times3.2

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

    7. Simplified2.2

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

    if -2.7540332723157e-316 < (/ (* x y) z) < 0.0 or 3.909153179489648e+266 < (/ (* x y) z)

    1. Initial program 18.8

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

    3. Applied *-un-lft-identity18.8

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

    4. Applied times-frac2.1

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

    5. Simplified2.1

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -2.75403327231568085421125185005337842666 \cdot 10^{-316}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 0.0:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 3.90915317948964794762777056224645120804 \cdot 10^{266}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(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))