Average Error: 15.1 → 0.9
Time: 3.6m
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.884682577215762039880854428140955206399 \cdot 10^{200}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.847656812384934442156413516898082202275 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.740047883140276970193031087160782955638 \cdot 10^{-240}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.072656266341375744037857515166265409716 \cdot 10^{86}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.884682577215762039880854428140955206399 \cdot 10^{200}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.847656812384934442156413516898082202275 \cdot 10^{-240}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 2.740047883140276970193031087160782955638 \cdot 10^{-240}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 2.072656266341375744037857515166265409716 \cdot 10^{86}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r137094131 = x;
        double r137094132 = y;
        double r137094133 = z;
        double r137094134 = r137094132 / r137094133;
        double r137094135 = t;
        double r137094136 = r137094134 * r137094135;
        double r137094137 = r137094136 / r137094135;
        double r137094138 = r137094131 * r137094137;
        return r137094138;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r137094139 = y;
        double r137094140 = z;
        double r137094141 = r137094139 / r137094140;
        double r137094142 = -1.884682577215762e+200;
        bool r137094143 = r137094141 <= r137094142;
        double r137094144 = x;
        double r137094145 = r137094139 * r137094144;
        double r137094146 = r137094145 / r137094140;
        double r137094147 = -1.8476568123849344e-240;
        bool r137094148 = r137094141 <= r137094147;
        double r137094149 = r137094144 * r137094141;
        double r137094150 = 2.740047883140277e-240;
        bool r137094151 = r137094141 <= r137094150;
        double r137094152 = 2.0726562663413757e+86;
        bool r137094153 = r137094141 <= r137094152;
        double r137094154 = r137094153 ? r137094149 : r137094146;
        double r137094155 = r137094151 ? r137094146 : r137094154;
        double r137094156 = r137094148 ? r137094149 : r137094155;
        double r137094157 = r137094143 ? r137094146 : r137094156;
        return r137094157;
}

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) < -1.884682577215762e+200 or -1.8476568123849344e-240 < (/ y z) < 2.740047883140277e-240 or 2.0726562663413757e+86 < (/ y z)

    1. Initial program 24.9

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

    2. Simplified14.6

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

    4. Applied add-cube-cbrt15.1

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

    5. Applied *-un-lft-identity15.1

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

    6. Applied times-frac15.1

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

    7. Applied associate-*r*4.5

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

    8. Simplified4.5

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

    10. Applied *-un-lft-identity4.5

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

    11. Applied times-frac4.5

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

    12. Applied associate-*l*4.3

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

    14. Applied frac-times2.6

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

    15. Applied frac-times2.6

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

    16. Simplified2.6

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

    17. Simplified1.9

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

    if -1.884682577215762e+200 < (/ y z) < -1.8476568123849344e-240 or 2.740047883140277e-240 < (/ y z) < 2.0726562663413757e+86

    1. Initial program 8.2

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

    2. Simplified0.2

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.884682577215762039880854428140955206399 \cdot 10^{200}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.847656812384934442156413516898082202275 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.740047883140276970193031087160782955638 \cdot 10^{-240}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.072656266341375744037857515166265409716 \cdot 10^{86}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))