Average Error: 15.1 → 1.0
Time: 14.0s
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 r9810184 = x;
        double r9810185 = y;
        double r9810186 = z;
        double r9810187 = r9810185 / r9810186;
        double r9810188 = t;
        double r9810189 = r9810187 * r9810188;
        double r9810190 = r9810189 / r9810188;
        double r9810191 = r9810184 * r9810190;
        return r9810191;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r9810192 = y;
        double r9810193 = z;
        double r9810194 = r9810192 / r9810193;
        double r9810195 = -2.3161828153264955e+221;
        bool r9810196 = r9810194 <= r9810195;
        double r9810197 = x;
        double r9810198 = r9810197 / r9810193;
        double r9810199 = r9810192 * r9810198;
        double r9810200 = -4.4642773403213894e-101;
        bool r9810201 = r9810194 <= r9810200;
        double r9810202 = r9810194 * r9810197;
        double r9810203 = 9.802087804866568e-279;
        bool r9810204 = r9810194 <= r9810203;
        double r9810205 = 1.7035288058957e+120;
        bool r9810206 = r9810194 <= r9810205;
        double r9810207 = r9810193 / r9810197;
        double r9810208 = r9810192 / r9810207;
        double r9810209 = r9810206 ? r9810202 : r9810208;
        double r9810210 = r9810204 ? r9810199 : r9810209;
        double r9810211 = r9810201 ? r9810202 : r9810210;
        double r9810212 = r9810196 ? r9810199 : r9810211;
        return r9810212;
}

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 associate-*r/9.7

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

    6. Applied *-un-lft-identity9.7

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

    7. Applied *-commutative9.7

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

    8. Applied times-frac0.2

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

    9. Simplified0.2

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

    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 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))