Average Error: 14.5 → 1.2
Time: 24.9s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.040296445133371 \cdot 10^{+100}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.055113727860028 \cdot 10^{-267}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.6317441627659235 \cdot 10^{-223}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 5.262177855603427 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -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 5.262177855603427 \cdot 10^{+76}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r2995641 = x;
        double r2995642 = y;
        double r2995643 = z;
        double r2995644 = r2995642 / r2995643;
        double r2995645 = t;
        double r2995646 = r2995644 * r2995645;
        double r2995647 = r2995646 / r2995645;
        double r2995648 = r2995641 * r2995647;
        return r2995648;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r2995649 = y;
        double r2995650 = z;
        double r2995651 = r2995649 / r2995650;
        double r2995652 = -1.040296445133371e+100;
        bool r2995653 = r2995651 <= r2995652;
        double r2995654 = x;
        double r2995655 = r2995654 / r2995650;
        double r2995656 = r2995649 * r2995655;
        double r2995657 = -6.055113727860028e-267;
        bool r2995658 = r2995651 <= r2995657;
        double r2995659 = r2995651 * r2995654;
        double r2995660 = 1.6317441627659235e-223;
        bool r2995661 = r2995651 <= r2995660;
        double r2995662 = 5.262177855603427e+76;
        bool r2995663 = r2995651 <= r2995662;
        double r2995664 = r2995650 / r2995649;
        double r2995665 = r2995654 / r2995664;
        double r2995666 = r2995650 / r2995654;
        double r2995667 = r2995649 / r2995666;
        double r2995668 = r2995663 ? r2995665 : r2995667;
        double r2995669 = r2995661 ? r2995656 : r2995668;
        double r2995670 = r2995658 ? r2995659 : r2995669;
        double r2995671 = r2995653 ? r2995656 : r2995670;
        return r2995671;
}

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

    1. Initial program 21.6

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

    2. Simplified1.3

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

    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. Taylor expanded around -inf 9.1

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

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

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

    6. Applied times-frac0.2

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

    7. Simplified0.2

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

    if 1.6317441627659235e-223 < (/ y z) < 5.262177855603427e+76

    1. Initial program 6.2

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

    2. Simplified8.9

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

    3. Taylor expanded around -inf 9.8

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

    5. Applied clear-num10.2

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

    6. Taylor expanded around 0 9.8

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

    8. Applied associate-/l*0.2

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

    if 5.262177855603427e+76 < (/ y z)

    1. Initial program 25.0

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

    2. Simplified4.7

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

    3. Taylor expanded around -inf 4.8

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

    5. Applied clear-num4.9

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

    7. Applied *-un-lft-identity4.9

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

    8. Applied add-sqr-sqrt4.9

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

    9. Applied times-frac4.9

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

    10. Simplified4.9

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

    11. Simplified4.8

      \[\leadsto 1 \cdot \color{blue}{\frac{y}{\frac{z}{x}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.040296445133371 \cdot 10^{+100}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.055113727860028 \cdot 10^{-267}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.6317441627659235 \cdot 10^{-223}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 5.262177855603427 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019130 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))