Average Error: 14.9 → 5.8
Time: 9.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le 1.082951294425128758406258396966231074708 \cdot 10^{128}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\sqrt{z}} \cdot \frac{x}{\sqrt{z}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;z \le 1.082951294425128758406258396966231074708 \cdot 10^{128}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r81936 = x;
        double r81937 = y;
        double r81938 = z;
        double r81939 = r81937 / r81938;
        double r81940 = t;
        double r81941 = r81939 * r81940;
        double r81942 = r81941 / r81940;
        double r81943 = r81936 * r81942;
        return r81943;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r81944 = z;
        double r81945 = 1.0829512944251288e+128;
        bool r81946 = r81944 <= r81945;
        double r81947 = y;
        double r81948 = x;
        double r81949 = r81947 * r81948;
        double r81950 = r81949 / r81944;
        double r81951 = sqrt(r81944);
        double r81952 = r81947 / r81951;
        double r81953 = r81948 / r81951;
        double r81954 = r81952 * r81953;
        double r81955 = r81946 ? r81950 : r81954;
        return r81955;
}

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 z < 1.0829512944251288e+128

    1. Initial program 15.5

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

    2. Simplified5.9

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

    if 1.0829512944251288e+128 < z

    1. Initial program 12.4

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

    2. Simplified6.7

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

    4. Applied add-sqr-sqrt6.9

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

    5. Applied times-frac5.2

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

  4. Final simplification5.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le 1.082951294425128758406258396966231074708 \cdot 10^{128}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\sqrt{z}} \cdot \frac{x}{\sqrt{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 
(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)))