Average Error: 14.5 → 0.6
Time: 13.1s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.088450935899302 \cdot 10^{+226}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -2.5749346451873716 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 4.6204979673822 \cdot 10^{-317}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 4.2714341334416977 \cdot 10^{+201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -5.088450935899302 \cdot 10^{+226}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -2.5749346451873716 \cdot 10^{-156}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 4.6204979673822 \cdot 10^{-317}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 4.2714341334416977 \cdot 10^{+201}:\\
\;\;\;\;\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 r4449566 = x;
        double r4449567 = y;
        double r4449568 = z;
        double r4449569 = r4449567 / r4449568;
        double r4449570 = t;
        double r4449571 = r4449569 * r4449570;
        double r4449572 = r4449571 / r4449570;
        double r4449573 = r4449566 * r4449572;
        return r4449573;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r4449574 = y;
        double r4449575 = z;
        double r4449576 = r4449574 / r4449575;
        double r4449577 = -5.088450935899302e+226;
        bool r4449578 = r4449576 <= r4449577;
        double r4449579 = x;
        double r4449580 = r4449579 / r4449575;
        double r4449581 = r4449574 * r4449580;
        double r4449582 = -2.5749346451873716e-156;
        bool r4449583 = r4449576 <= r4449582;
        double r4449584 = r4449576 * r4449579;
        double r4449585 = 4.6204979673822e-317;
        bool r4449586 = r4449576 <= r4449585;
        double r4449587 = r4449579 * r4449574;
        double r4449588 = r4449587 / r4449575;
        double r4449589 = 4.2714341334416977e+201;
        bool r4449590 = r4449576 <= r4449589;
        double r4449591 = r4449575 / r4449574;
        double r4449592 = r4449579 / r4449591;
        double r4449593 = r4449590 ? r4449592 : r4449581;
        double r4449594 = r4449586 ? r4449588 : r4449593;
        double r4449595 = r4449583 ? r4449584 : r4449594;
        double r4449596 = r4449578 ? r4449581 : r4449595;
        return r4449596;
}

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) < -5.088450935899302e+226 or 4.2714341334416977e+201 < (/ y z)

    1. Initial program 41.2

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

    2. Simplified0.9

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

    if -5.088450935899302e+226 < (/ y z) < -2.5749346451873716e-156

    1. Initial program 8.0

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

    2. Simplified9.6

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

    3. Taylor expanded around 0 9.2

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

    5. Applied *-un-lft-identity9.2

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

    6. Applied times-frac0.3

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

    7. Simplified0.3

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

    if -2.5749346451873716e-156 < (/ y z) < 4.6204979673822e-317

    1. Initial program 17.5

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

    2. Simplified0.6

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

    3. Taylor expanded around 0 0.9

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

    if 4.6204979673822e-317 < (/ y z) < 4.2714341334416977e+201

    1. Initial program 9.0

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

    2. Simplified7.7

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

    3. Taylor expanded around 0 8.2

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

    5. Applied associate-/l*0.5

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.088450935899302 \cdot 10^{+226}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -2.5749346451873716 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 4.6204979673822 \cdot 10^{-317}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 4.2714341334416977 \cdot 10^{+201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))