Average Error: 15.1 → 6.0
Time: 13.3s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.456893094179093804320322909204701959778 \cdot 10^{-222}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \le -1.998153801628733335171500404420370674566 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \le 8.447680461540099603836085647567339379828 \cdot 10^{-193}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \le 1.21944214684399880068881121045408236628 \cdot 10^{120}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.456893094179093804320322909204701959778 \cdot 10^{-222}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;z \le -1.998153801628733335171500404420370674566 \cdot 10^{-247}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;z \le 8.447680461540099603836085647567339379828 \cdot 10^{-193}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;z \le 1.21944214684399880068881121045408236628 \cdot 10^{120}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r4476285 = x;
        double r4476286 = y;
        double r4476287 = z;
        double r4476288 = r4476286 / r4476287;
        double r4476289 = t;
        double r4476290 = r4476288 * r4476289;
        double r4476291 = r4476290 / r4476289;
        double r4476292 = r4476285 * r4476291;
        return r4476292;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r4476293 = z;
        double r4476294 = -5.456893094179094e-222;
        bool r4476295 = r4476293 <= r4476294;
        double r4476296 = x;
        double r4476297 = y;
        double r4476298 = r4476296 * r4476297;
        double r4476299 = r4476298 / r4476293;
        double r4476300 = -1.9981538016287333e-247;
        bool r4476301 = r4476293 <= r4476300;
        double r4476302 = r4476296 / r4476293;
        double r4476303 = r4476297 * r4476302;
        double r4476304 = 8.4476804615401e-193;
        bool r4476305 = r4476293 <= r4476304;
        double r4476306 = 1.2194421468439988e+120;
        bool r4476307 = r4476293 <= r4476306;
        double r4476308 = r4476293 / r4476296;
        double r4476309 = r4476297 / r4476308;
        double r4476310 = r4476307 ? r4476309 : r4476299;
        double r4476311 = r4476305 ? r4476299 : r4476310;
        double r4476312 = r4476301 ? r4476303 : r4476311;
        double r4476313 = r4476295 ? r4476299 : r4476312;
        return r4476313;
}

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 z < -5.456893094179094e-222 or -1.9981538016287333e-247 < z < 8.4476804615401e-193 or 1.2194421468439988e+120 < z

    1. Initial program 15.2

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

    2. Simplified6.7

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

    if -5.456893094179094e-222 < z < -1.9981538016287333e-247

    1. Initial program 23.4

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

    2. Simplified14.4

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

    4. Applied associate-/l*13.8

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

    6. Applied associate-/r/8.7

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

    if 8.4476804615401e-193 < z < 1.2194421468439988e+120

    1. Initial program 14.4

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

    2. Simplified4.5

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

    4. Applied add-cube-cbrt5.4

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

    5. Applied associate-/r*5.4

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

    7. Applied *-un-lft-identity5.4

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

    8. Applied cbrt-prod5.4

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

    9. Applied *-un-lft-identity5.4

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

    10. Applied times-frac5.4

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

    11. Simplified5.4

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

    12. Simplified3.7

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

  4. Final simplification6.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.456893094179093804320322909204701959778 \cdot 10^{-222}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \le -1.998153801628733335171500404420370674566 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \le 8.447680461540099603836085647567339379828 \cdot 10^{-193}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \le 1.21944214684399880068881121045408236628 \cdot 10^{120}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +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)))