Average Error: 14.7 → 0.3
Time: 12.4s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.1673826862143979 \cdot 10^{+231}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.897283238983837 \cdot 10^{-237}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.1115659814397386 \cdot 10^{+232}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.1673826862143979 \cdot 10^{+231}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.897283238983837 \cdot 10^{-237}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\mathbf{elif}\;\frac{y}{z} \le 1.1115659814397386 \cdot 10^{+232}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r4179805 = x;
        double r4179806 = y;
        double r4179807 = z;
        double r4179808 = r4179806 / r4179807;
        double r4179809 = t;
        double r4179810 = r4179808 * r4179809;
        double r4179811 = r4179810 / r4179809;
        double r4179812 = r4179805 * r4179811;
        return r4179812;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r4179813 = y;
        double r4179814 = z;
        double r4179815 = r4179813 / r4179814;
        double r4179816 = -1.1673826862143979e+231;
        bool r4179817 = r4179815 <= r4179816;
        double r4179818 = x;
        double r4179819 = r4179818 * r4179813;
        double r4179820 = r4179819 / r4179814;
        double r4179821 = -1.897283238983837e-237;
        bool r4179822 = r4179815 <= r4179821;
        double r4179823 = r4179815 * r4179818;
        double r4179824 = 0.0;
        bool r4179825 = r4179815 <= r4179824;
        double r4179826 = r4179814 / r4179818;
        double r4179827 = r4179813 / r4179826;
        double r4179828 = 1.1115659814397386e+232;
        bool r4179829 = r4179815 <= r4179828;
        double r4179830 = r4179818 / r4179814;
        double r4179831 = r4179813 * r4179830;
        double r4179832 = r4179829 ? r4179823 : r4179831;
        double r4179833 = r4179825 ? r4179827 : r4179832;
        double r4179834 = r4179822 ? r4179823 : r4179833;
        double r4179835 = r4179817 ? r4179820 : r4179834;
        return r4179835;
}

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 4 regimes

  2. if (/ y z) < -1.1673826862143979e+231

    1. Initial program 47.5

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

    2. Simplified0.7

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

    4. Applied associate-*r/0.7

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

    if -1.1673826862143979e+231 < (/ y z) < -1.897283238983837e-237 or 0.0 < (/ y z) < 1.1115659814397386e+232

    1. Initial program 9.3

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

    2. Simplified8.9

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

    4. Applied associate-*r/7.8

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

    6. Applied associate-/l*8.8

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

    8. Applied associate-/r/0.3

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

    if -1.897283238983837e-237 < (/ y z) < 0.0

    1. Initial program 19.5

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

    2. Simplified0.2

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

    4. Applied associate-*r/0.2

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

    6. Applied associate-/l*0.1

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

    if 1.1115659814397386e+232 < (/ y z)

    1. Initial program 42.8

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

    2. Simplified0.8

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.1673826862143979 \cdot 10^{+231}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.897283238983837 \cdot 10^{-237}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.1115659814397386 \cdot 10^{+232}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))