Average Error: 14.5 → 1.0
Time: 22.0s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.040296445133371 \cdot 10^{+100}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.055113727860028 \cdot 10^{-267}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.6317441627659235 \cdot 10^{-223}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 5.528315742714586 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.040296445133371 \cdot 10^{+100}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -6.055113727860028 \cdot 10^{-267}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 1.6317441627659235 \cdot 10^{-223}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 5.528315742714586 \cdot 10^{+102}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r3040721 = x;
        double r3040722 = y;
        double r3040723 = z;
        double r3040724 = r3040722 / r3040723;
        double r3040725 = t;
        double r3040726 = r3040724 * r3040725;
        double r3040727 = r3040726 / r3040725;
        double r3040728 = r3040721 * r3040727;
        return r3040728;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3040729 = y;
        double r3040730 = z;
        double r3040731 = r3040729 / r3040730;
        double r3040732 = -1.040296445133371e+100;
        bool r3040733 = r3040731 <= r3040732;
        double r3040734 = x;
        double r3040735 = r3040734 / r3040730;
        double r3040736 = r3040729 * r3040735;
        double r3040737 = -6.055113727860028e-267;
        bool r3040738 = r3040731 <= r3040737;
        double r3040739 = r3040731 * r3040734;
        double r3040740 = 1.6317441627659235e-223;
        bool r3040741 = r3040731 <= r3040740;
        double r3040742 = 5.528315742714586e+102;
        bool r3040743 = r3040731 <= r3040742;
        double r3040744 = r3040730 / r3040729;
        double r3040745 = r3040734 / r3040744;
        double r3040746 = r3040743 ? r3040745 : r3040736;
        double r3040747 = r3040741 ? r3040736 : r3040746;
        double r3040748 = r3040738 ? r3040739 : r3040747;
        double r3040749 = r3040733 ? r3040736 : r3040748;
        return r3040749;
}

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) < -1.040296445133371e+100 or -6.055113727860028e-267 < (/ y z) < 1.6317441627659235e-223 or 5.528315742714586e+102 < (/ y z)

    1. Initial program 22.9

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

    2. Simplified2.1

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

    if -1.040296445133371e+100 < (/ y z) < -6.055113727860028e-267

    1. Initial program 8.7

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

    2. Simplified8.2

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

    4. Applied associate-*l/9.1

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

    6. Applied *-un-lft-identity9.1

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

    7. Applied times-frac0.2

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

    8. Simplified0.2

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

    if 1.6317441627659235e-223 < (/ y z) < 5.528315742714586e+102

    1. Initial program 6.7

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

    2. Simplified8.8

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

    4. Applied associate-*l/10.0

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

    6. Applied associate-/l*0.2

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.040296445133371 \cdot 10^{+100}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.055113727860028 \cdot 10^{-267}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.6317441627659235 \cdot 10^{-223}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 5.528315742714586 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019130 +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)))