Average Error: 15.1 → 1.0
Time: 14.7s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.3161828153264955 \cdot 10^{+221}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -4.4642773403213894 \cdot 10^{-101}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 9.802087804866568 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.7035288058957 \cdot 10^{+120}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -2.3161828153264955 \cdot 10^{+221}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -4.4642773403213894 \cdot 10^{-101}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 9.802087804866568 \cdot 10^{-279}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 1.7035288058957 \cdot 10^{+120}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r4129906 = x;
        double r4129907 = y;
        double r4129908 = z;
        double r4129909 = r4129907 / r4129908;
        double r4129910 = t;
        double r4129911 = r4129909 * r4129910;
        double r4129912 = r4129911 / r4129910;
        double r4129913 = r4129906 * r4129912;
        return r4129913;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r4129914 = y;
        double r4129915 = z;
        double r4129916 = r4129914 / r4129915;
        double r4129917 = -2.3161828153264955e+221;
        bool r4129918 = r4129916 <= r4129917;
        double r4129919 = x;
        double r4129920 = r4129919 / r4129915;
        double r4129921 = r4129914 * r4129920;
        double r4129922 = -4.4642773403213894e-101;
        bool r4129923 = r4129916 <= r4129922;
        double r4129924 = r4129916 * r4129919;
        double r4129925 = 9.802087804866568e-279;
        bool r4129926 = r4129916 <= r4129925;
        double r4129927 = 1.7035288058957e+120;
        bool r4129928 = r4129916 <= r4129927;
        double r4129929 = r4129915 / r4129919;
        double r4129930 = r4129914 / r4129929;
        double r4129931 = r4129928 ? r4129924 : r4129930;
        double r4129932 = r4129926 ? r4129921 : r4129931;
        double r4129933 = r4129923 ? r4129924 : r4129932;
        double r4129934 = r4129918 ? r4129921 : r4129933;
        return r4129934;
}

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) < -2.3161828153264955e+221 or -4.4642773403213894e-101 < (/ y z) < 9.802087804866568e-279

    1. Initial program 21.4

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

    2. Simplified1.6

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

    if -2.3161828153264955e+221 < (/ y z) < -4.4642773403213894e-101 or 9.802087804866568e-279 < (/ y z) < 1.7035288058957e+120

    1. Initial program 7.6

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

    2. Simplified9.6

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

    4. Applied *-un-lft-identity9.6

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

    5. Applied associate-/r*9.6

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

    6. Applied associate-*r/9.7

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

    7. Simplified9.7

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

    9. Applied clear-num10.1

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

    11. Applied *-commutative10.1

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

    12. Applied associate-/r*0.8

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

    13. Applied associate-/r/0.3

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

    14. Simplified0.2

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

    if 1.7035288058957e+120 < (/ y z)

    1. Initial program 31.1

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

    2. Simplified2.6

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

    4. Applied clear-num3.0

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

    5. Applied un-div-inv2.6

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.3161828153264955 \cdot 10^{+221}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -4.4642773403213894 \cdot 10^{-101}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 9.802087804866568 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.7035288058957 \cdot 10^{+120}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 +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)))