Average Error: 14.8 → 0.5
Time: 1.8s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.6183489977482823 \cdot 10^{236}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.8792362608384231 \cdot 10^{-264}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.06689610291439 \cdot 10^{-310}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le 8.69850988828769301 \cdot 10^{221}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -4.6183489977482823 \cdot 10^{236}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -6.8792362608384231 \cdot 10^{-264}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 1.06689610291439 \cdot 10^{-310}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\mathbf{elif}\;\frac{y}{z} \le 8.69850988828769301 \cdot 10^{221}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r78667 = x;
        double r78668 = y;
        double r78669 = z;
        double r78670 = r78668 / r78669;
        double r78671 = t;
        double r78672 = r78670 * r78671;
        double r78673 = r78672 / r78671;
        double r78674 = r78667 * r78673;
        return r78674;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r78675 = y;
        double r78676 = z;
        double r78677 = r78675 / r78676;
        double r78678 = -4.618348997748282e+236;
        bool r78679 = r78677 <= r78678;
        double r78680 = x;
        double r78681 = r78680 * r78675;
        double r78682 = 1.0;
        double r78683 = r78682 / r78676;
        double r78684 = r78681 * r78683;
        double r78685 = -6.879236260838423e-264;
        bool r78686 = r78677 <= r78685;
        double r78687 = r78680 * r78677;
        double r78688 = 1.0668961029144e-310;
        bool r78689 = r78677 <= r78688;
        double r78690 = r78676 / r78681;
        double r78691 = r78682 / r78690;
        double r78692 = 8.698509888287693e+221;
        bool r78693 = r78677 <= r78692;
        double r78694 = r78676 / r78675;
        double r78695 = r78680 / r78694;
        double r78696 = r78693 ? r78695 : r78684;
        double r78697 = r78689 ? r78691 : r78696;
        double r78698 = r78686 ? r78687 : r78697;
        double r78699 = r78679 ? r78684 : r78698;
        return r78699;
}

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) < -4.618348997748282e+236 or 8.698509888287693e+221 < (/ y z)

    1. Initial program 45.8

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

    2. Simplified33.2

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

    4. Applied div-inv33.3

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]

    5. Applied associate-*r*1.1

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]

    if -4.618348997748282e+236 < (/ y z) < -6.879236260838423e-264

    1. Initial program 9.7

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

    2. Simplified0.2

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

    if -6.879236260838423e-264 < (/ y z) < 1.0668961029144e-310

    1. Initial program 19.2

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

    2. Simplified16.5

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

    4. Applied associate-*r/0.1

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

    6. Applied clear-num0.9

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

    if 1.0668961029144e-310 < (/ y z) < 8.698509888287693e+221

    1. Initial program 9.0

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

    2. Simplified0.2

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

    4. Applied associate-*r/8.6

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

    6. Applied associate-/l*0.3

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.6183489977482823 \cdot 10^{236}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.8792362608384231 \cdot 10^{-264}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.06689610291439 \cdot 10^{-310}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le 8.69850988828769301 \cdot 10^{221}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))