Average Error: 14.5 → 3.4
Time: 26.4s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le 8.413937948676428647326966542545809971377 \cdot 10^{-321} \lor \neg \left(\frac{y}{z} \le 4.894548959283928660268685456970986818461 \cdot 10^{144}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le 8.413937948676428647326966542545809971377 \cdot 10^{-321} \lor \neg \left(\frac{y}{z} \le 4.894548959283928660268685456970986818461 \cdot 10^{144}\right):\\
\;\;\;\;y \cdot \frac{x}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r81810 = x;
        double r81811 = y;
        double r81812 = z;
        double r81813 = r81811 / r81812;
        double r81814 = t;
        double r81815 = r81813 * r81814;
        double r81816 = r81815 / r81814;
        double r81817 = r81810 * r81816;
        return r81817;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r81818 = y;
        double r81819 = z;
        double r81820 = r81818 / r81819;
        double r81821 = 8.4139379486764e-321;
        bool r81822 = r81820 <= r81821;
        double r81823 = 4.894548959283929e+144;
        bool r81824 = r81820 <= r81823;
        double r81825 = !r81824;
        bool r81826 = r81822 || r81825;
        double r81827 = x;
        double r81828 = r81827 / r81819;
        double r81829 = r81818 * r81828;
        double r81830 = r81819 / r81818;
        double r81831 = r81827 / r81830;
        double r81832 = r81826 ? r81829 : r81831;
        return r81832;
}

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) < 8.4139379486764e-321 or 4.894548959283929e+144 < (/ y z)

    1. Initial program 17.4

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

    2. Simplified9.2

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

    4. Applied div-inv9.3

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

    5. Applied associate-*l*4.9

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

    6. Simplified4.8

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

    if 8.4139379486764e-321 < (/ y z) < 4.894548959283929e+144

    1. Initial program 8.9

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

    2. Simplified0.4

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

    4. Applied div-inv0.4

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

    5. Applied associate-*l*8.7

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

    6. Simplified8.6

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

    8. Applied *-un-lft-identity8.6

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

    9. Applied associate-*l*8.6

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

    10. Simplified8.0

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

    12. Applied associate-/l*0.6

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

  4. Final simplification3.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le 8.413937948676428647326966542545809971377 \cdot 10^{-321} \lor \neg \left(\frac{y}{z} \le 4.894548959283928660268685456970986818461 \cdot 10^{144}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019304 
(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)))