Average Error: 14.0 → 5.4
Time: 10.0s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -9.484727702764666 \cdot 10^{+241}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \le -2.333076602971364 \cdot 10^{-69}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;y \le 6.356954331308777 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \le 5.784716735603109 \cdot 10^{+161}:\\ \;\;\;\;\left(\frac{y}{\sqrt[3]{z}} \cdot \frac{x}{\sqrt[3]{z}}\right) \cdot \frac{1}{\sqrt[3]{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -9.484727702764666 \cdot 10^{+241}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;y \le -2.333076602971364 \cdot 10^{-69}:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\

\mathbf{elif}\;y \le 6.356954331308777 \cdot 10^{-261}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;y \le 5.784716735603109 \cdot 10^{+161}:\\
\;\;\;\;\left(\frac{y}{\sqrt[3]{z}} \cdot \frac{x}{\sqrt[3]{z}}\right) \cdot \frac{1}{\sqrt[3]{z}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r3178140 = x;
        double r3178141 = y;
        double r3178142 = z;
        double r3178143 = r3178141 / r3178142;
        double r3178144 = t;
        double r3178145 = r3178143 * r3178144;
        double r3178146 = r3178145 / r3178144;
        double r3178147 = r3178140 * r3178146;
        return r3178147;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3178148 = y;
        double r3178149 = -9.484727702764666e+241;
        bool r3178150 = r3178148 <= r3178149;
        double r3178151 = x;
        double r3178152 = r3178151 * r3178148;
        double r3178153 = z;
        double r3178154 = r3178152 / r3178153;
        double r3178155 = -2.333076602971364e-69;
        bool r3178156 = r3178148 <= r3178155;
        double r3178157 = 1.0;
        double r3178158 = r3178153 / r3178151;
        double r3178159 = r3178158 / r3178148;
        double r3178160 = r3178157 / r3178159;
        double r3178161 = 6.356954331308777e-261;
        bool r3178162 = r3178148 <= r3178161;
        double r3178163 = 5.784716735603109e+161;
        bool r3178164 = r3178148 <= r3178163;
        double r3178165 = cbrt(r3178153);
        double r3178166 = r3178148 / r3178165;
        double r3178167 = r3178151 / r3178165;
        double r3178168 = r3178166 * r3178167;
        double r3178169 = r3178157 / r3178165;
        double r3178170 = r3178168 * r3178169;
        double r3178171 = r3178164 ? r3178170 : r3178154;
        double r3178172 = r3178162 ? r3178154 : r3178171;
        double r3178173 = r3178156 ? r3178160 : r3178172;
        double r3178174 = r3178150 ? r3178154 : r3178173;
        return r3178174;
}

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 3 regimes

  2. if y < -9.484727702764666e+241 or -2.333076602971364e-69 < y < 6.356954331308777e-261 or 5.784716735603109e+161 < y

    1. Initial program 14.7

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

    2. Simplified8.2

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

    4. Applied div-inv8.3

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
    5. Using strategy rm

    6. Applied un-div-inv8.2

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

    if -9.484727702764666e+241 < y < -2.333076602971364e-69

    1. Initial program 15.0

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

    2. Simplified5.7

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

    4. Applied clear-num6.1

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

    6. Applied associate-/r*5.2

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

    if 6.356954331308777e-261 < y < 5.784716735603109e+161

    1. Initial program 12.7

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

    2. Simplified4.0

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

    4. Applied div-inv4.1

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt4.8

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

    7. Applied *-un-lft-identity4.8

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

    8. Applied times-frac4.8

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

    9. Applied associate-*r*4.8

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

    10. Simplified2.5

      \[\leadsto \color{blue}{\left(\frac{y}{\sqrt[3]{z}} \cdot \frac{x}{\sqrt[3]{z}}\right)} \cdot \frac{1}{\sqrt[3]{z}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification5.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -9.484727702764666 \cdot 10^{+241}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \le -2.333076602971364 \cdot 10^{-69}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;y \le 6.356954331308777 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \le 5.784716735603109 \cdot 10^{+161}:\\ \;\;\;\;\left(\frac{y}{\sqrt[3]{z}} \cdot \frac{x}{\sqrt[3]{z}}\right) \cdot \frac{1}{\sqrt[3]{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))