Average Error: 14.5 → 0.5
Time: 3.7s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -6.122731566035475311671418161909773301552 \cdot 10^{157} \lor \neg \left(\frac{y}{z} \le -2.242439350440375267697031348628742827796 \cdot 10^{-179} \lor \neg \left(\frac{y}{z} \le 5.129556799950046333853278890491110988102 \cdot 10^{-271} \lor \neg \left(\frac{y}{z} \le 1.795095217187765936797771641264103283314 \cdot 10^{286}\right)\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -6.122731566035475311671418161909773301552 \cdot 10^{157} \lor \neg \left(\frac{y}{z} \le -2.242439350440375267697031348628742827796 \cdot 10^{-179} \lor \neg \left(\frac{y}{z} \le 5.129556799950046333853278890491110988102 \cdot 10^{-271} \lor \neg \left(\frac{y}{z} \le 1.795095217187765936797771641264103283314 \cdot 10^{286}\right)\right)\right):\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r85229 = x;
        double r85230 = y;
        double r85231 = z;
        double r85232 = r85230 / r85231;
        double r85233 = t;
        double r85234 = r85232 * r85233;
        double r85235 = r85234 / r85233;
        double r85236 = r85229 * r85235;
        return r85236;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r85237 = y;
        double r85238 = z;
        double r85239 = r85237 / r85238;
        double r85240 = -6.122731566035475e+157;
        bool r85241 = r85239 <= r85240;
        double r85242 = -2.2424393504403753e-179;
        bool r85243 = r85239 <= r85242;
        double r85244 = 5.129556799950046e-271;
        bool r85245 = r85239 <= r85244;
        double r85246 = 1.795095217187766e+286;
        bool r85247 = r85239 <= r85246;
        double r85248 = !r85247;
        bool r85249 = r85245 || r85248;
        double r85250 = !r85249;
        bool r85251 = r85243 || r85250;
        double r85252 = !r85251;
        bool r85253 = r85241 || r85252;
        double r85254 = x;
        double r85255 = r85254 * r85237;
        double r85256 = r85255 / r85238;
        double r85257 = r85254 * r85239;
        double r85258 = r85253 ? r85256 : r85257;
        return r85258;
}

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) < -6.122731566035475e+157 or -2.2424393504403753e-179 < (/ y z) < 5.129556799950046e-271 or 1.795095217187766e+286 < (/ y z)

    1. Initial program 24.3

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

    2. Simplified16.0

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

    4. Applied *-un-lft-identity16.0

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

    5. Applied add-cube-cbrt16.4

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

    6. Applied times-frac16.4

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

    7. Applied associate-*r*4.3

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

    8. Simplified4.3

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

    10. Applied add-cube-cbrt4.5

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

    12. Applied associate-*r/1.9

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

    13. Simplified1.0

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

    if -6.122731566035475e+157 < (/ y z) < -2.2424393504403753e-179 or 5.129556799950046e-271 < (/ y z) < 1.795095217187766e+286

    1. Initial program 9.0

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

    2. Simplified0.2

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -6.122731566035475311671418161909773301552 \cdot 10^{157} \lor \neg \left(\frac{y}{z} \le -2.242439350440375267697031348628742827796 \cdot 10^{-179} \lor \neg \left(\frac{y}{z} \le 5.129556799950046333853278890491110988102 \cdot 10^{-271} \lor \neg \left(\frac{y}{z} \le 1.795095217187765936797771641264103283314 \cdot 10^{286}\right)\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(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)))