Average Error: 6.2 → 6.3
Time: 10.8s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le 2.39259709741611536 \cdot 10^{-307}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;z \le 1.08745764864859695 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \le 1.4101106747621872 \cdot 10^{212}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le 2.39259709741611536 \cdot 10^{-307}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

\mathbf{elif}\;z \le 1.08745764864859695 \cdot 10^{-70}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;z \le 1.4101106747621872 \cdot 10^{212}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

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

\end{array}
double f(double x, double y, double z) {
        double r457247 = x;
        double r457248 = y;
        double r457249 = r457247 * r457248;
        double r457250 = z;
        double r457251 = r457249 / r457250;
        return r457251;
}
↓
double f(double x, double y, double z) {
        double r457252 = z;
        double r457253 = 2.3925970974161154e-307;
        bool r457254 = r457252 <= r457253;
        double r457255 = x;
        double r457256 = r457255 / r457252;
        double r457257 = y;
        double r457258 = r457256 * r457257;
        double r457259 = 1.087457648648597e-70;
        bool r457260 = r457252 <= r457259;
        double r457261 = r457252 / r457257;
        double r457262 = r457255 / r457261;
        double r457263 = 1.4101106747621872e+212;
        bool r457264 = r457252 <= r457263;
        double r457265 = r457257 / r457252;
        double r457266 = r457255 * r457265;
        double r457267 = r457264 ? r457258 : r457266;
        double r457268 = r457260 ? r457262 : r457267;
        double r457269 = r457254 ? r457258 : r457268;
        return r457269;
}

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
Target6.2
Herbie6.3
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < 2.3925970974161154e-307 or 1.087457648648597e-70 < z < 1.4101106747621872e+212

    1. Initial program 5.3

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

    3. Applied *-un-lft-identity5.3

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

    4. Applied times-frac5.2

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

    5. Simplified5.2

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

    7. Applied *-un-lft-identity5.2

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

    8. Applied add-cube-cbrt6.0

      \[\leadsto x \cdot \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{1 \cdot z}\]

    9. Applied times-frac6.0

      \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{z}\right)}\]

    10. Applied associate-*r*4.4

      \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1}\right) \cdot \frac{\sqrt[3]{y}}{z}}\]

    11. Simplified4.4

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

    12. Taylor expanded around 0 5.3

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

    13. Simplified5.8

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

    if 2.3925970974161154e-307 < z < 1.087457648648597e-70

    1. Initial program 9.3

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

    3. Applied associate-/l*8.6

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

    if 1.4101106747621872e+212 < z

    1. Initial program 7.6

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

    3. Applied *-un-lft-identity7.6

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

    4. Applied times-frac7.2

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

    5. Simplified7.2

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

  4. Final simplification6.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le 2.39259709741611536 \cdot 10^{-307}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;z \le 1.08745764864859695 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \le 1.4101106747621872 \cdot 10^{212}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(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))