Average Error: 14.5 → 2.2
Time: 4.3s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.42110258613913981 \cdot 10^{-87} \lor \neg \left(\frac{y}{z} \le 1.1014995100088346 \cdot 10^{-297} \lor \neg \left(\frac{y}{z} \le 1.84201517993839439 \cdot 10^{192}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.42110258613913981 \cdot 10^{-87} \lor \neg \left(\frac{y}{z} \le 1.1014995100088346 \cdot 10^{-297} \lor \neg \left(\frac{y}{z} \le 1.84201517993839439 \cdot 10^{192}\right)\right):\\
\;\;\;\;x \cdot \frac{y}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r100795 = x;
        double r100796 = y;
        double r100797 = z;
        double r100798 = r100796 / r100797;
        double r100799 = t;
        double r100800 = r100798 * r100799;
        double r100801 = r100800 / r100799;
        double r100802 = r100795 * r100801;
        return r100802;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r100803 = y;
        double r100804 = z;
        double r100805 = r100803 / r100804;
        double r100806 = -1.4211025861391398e-87;
        bool r100807 = r100805 <= r100806;
        double r100808 = 1.1014995100088346e-297;
        bool r100809 = r100805 <= r100808;
        double r100810 = 1.8420151799383944e+192;
        bool r100811 = r100805 <= r100810;
        double r100812 = !r100811;
        bool r100813 = r100809 || r100812;
        double r100814 = !r100813;
        bool r100815 = r100807 || r100814;
        double r100816 = x;
        double r100817 = r100816 * r100805;
        double r100818 = r100816 * r100803;
        double r100819 = r100818 / r100804;
        double r100820 = r100815 ? r100817 : r100819;
        return r100820;
}

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 2 regimes

  2. if (/ y z) < -1.4211025861391398e-87 or 1.1014995100088346e-297 < (/ y z) < 1.8420151799383944e+192

    1. Initial program 11.1

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

    2. Simplified2.5

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

    if -1.4211025861391398e-87 < (/ y z) < 1.1014995100088346e-297 or 1.8420151799383944e+192 < (/ y z)

    1. Initial program 20.6

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

    2. Simplified12.1

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

    4. Applied add-cube-cbrt12.6

      \[\leadsto x \cdot \frac{y}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    5. Applied *-un-lft-identity12.6

      \[\leadsto x \cdot \frac{\color{blue}{1 \cdot y}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}\]

    6. Applied times-frac12.6

      \[\leadsto x \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}}\right)}\]

    7. Applied associate-*r*3.6

      \[\leadsto \color{blue}{\left(x \cdot \frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{y}{\sqrt[3]{z}}}\]

    8. Simplified3.6

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

    10. Applied *-un-lft-identity3.6

      \[\leadsto \color{blue}{\left(1 \cdot \frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)} \cdot \frac{y}{\sqrt[3]{z}}\]

    11. Applied associate-*l*3.6

      \[\leadsto \color{blue}{1 \cdot \left(\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}}\right)}\]

    12. Simplified1.8

      \[\leadsto 1 \cdot \color{blue}{\frac{x \cdot y}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.42110258613913981 \cdot 10^{-87} \lor \neg \left(\frac{y}{z} \le 1.1014995100088346 \cdot 10^{-297} \lor \neg \left(\frac{y}{z} \le 1.84201517993839439 \cdot 10^{192}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 
(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)))