Average Error: 14.3 → 2.2
Time: 22.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.0532464204699888 \cdot 10^{+209}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.588547053565423 \cdot 10^{-193}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 2.2740014914314757 \cdot 10^{-89}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.0532464204699888 \cdot 10^{+209}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -6.588547053565423 \cdot 10^{-193}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 2.2740014914314757 \cdot 10^{-89}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r2650279 = x;
        double r2650280 = y;
        double r2650281 = z;
        double r2650282 = r2650280 / r2650281;
        double r2650283 = t;
        double r2650284 = r2650282 * r2650283;
        double r2650285 = r2650284 / r2650283;
        double r2650286 = r2650279 * r2650285;
        return r2650286;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r2650287 = y;
        double r2650288 = z;
        double r2650289 = r2650287 / r2650288;
        double r2650290 = -1.0532464204699888e+209;
        bool r2650291 = r2650289 <= r2650290;
        double r2650292 = x;
        double r2650293 = r2650292 / r2650288;
        double r2650294 = r2650287 * r2650293;
        double r2650295 = -6.588547053565423e-193;
        bool r2650296 = r2650289 <= r2650295;
        double r2650297 = r2650289 * r2650292;
        double r2650298 = 2.2740014914314757e-89;
        bool r2650299 = r2650289 <= r2650298;
        double r2650300 = r2650292 * r2650287;
        double r2650301 = r2650300 / r2650288;
        double r2650302 = r2650299 ? r2650301 : r2650297;
        double r2650303 = r2650296 ? r2650297 : r2650302;
        double r2650304 = r2650291 ? r2650294 : r2650303;
        return r2650304;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -1.0532464204699888e+209

    1. Initial program 40.4

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

    2. Simplified0.4

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

    if -1.0532464204699888e+209 < (/ y z) < -6.588547053565423e-193 or 2.2740014914314757e-89 < (/ y z)

    1. Initial program 11.1

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

    2. Simplified8.8

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

    4. Applied div-inv8.9

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

    5. Applied associate-*l*2.9

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

    6. Simplified2.8

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

    if -6.588547053565423e-193 < (/ y z) < 2.2740014914314757e-89

    1. Initial program 15.7

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

    2. Simplified1.4

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

    4. Applied div-inv1.5

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

    5. Applied associate-*l*8.2

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

    6. Simplified8.1

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

    8. Applied *-un-lft-identity8.1

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

    9. Applied add-cube-cbrt8.6

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

    10. Applied times-frac8.6

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

    11. Applied associate-*r*2.8

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

    12. Simplified2.8

      \[\leadsto \color{blue}{\left(\left(x \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} \cdot \frac{\sqrt[3]{y}}{z}\]
    13. Using strategy rm

    14. Applied associate-*r/2.2

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

    15. Simplified1.6

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.0532464204699888 \cdot 10^{+209}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.588547053565423 \cdot 10^{-193}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 2.2740014914314757 \cdot 10^{-89}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))