Average Error: 15.4 → 1.0
Time: 14.7s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.057433920064963 \cdot 10^{133}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le -1.0665637347194774 \cdot 10^{-221} \lor \neg \left(\frac{y}{z} \le 1.5828563463705101 \cdot 10^{-127}\right) \land \frac{y}{z} \le 2.5905951762285947 \cdot 10^{176}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.057433920064963 \cdot 10^{133}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\mathbf{elif}\;\frac{y}{z} \le -1.0665637347194774 \cdot 10^{-221} \lor \neg \left(\frac{y}{z} \le 1.5828563463705101 \cdot 10^{-127}\right) \land \frac{y}{z} \le 2.5905951762285947 \cdot 10^{176}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r107221 = x;
        double r107222 = y;
        double r107223 = z;
        double r107224 = r107222 / r107223;
        double r107225 = t;
        double r107226 = r107224 * r107225;
        double r107227 = r107226 / r107225;
        double r107228 = r107221 * r107227;
        return r107228;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r107229 = y;
        double r107230 = z;
        double r107231 = r107229 / r107230;
        double r107232 = -1.057433920064963e+133;
        bool r107233 = r107231 <= r107232;
        double r107234 = 1.0;
        double r107235 = x;
        double r107236 = r107235 * r107229;
        double r107237 = r107230 / r107236;
        double r107238 = r107234 / r107237;
        double r107239 = -1.0665637347194774e-221;
        bool r107240 = r107231 <= r107239;
        double r107241 = 1.5828563463705101e-127;
        bool r107242 = r107231 <= r107241;
        double r107243 = !r107242;
        double r107244 = 2.5905951762285947e+176;
        bool r107245 = r107231 <= r107244;
        bool r107246 = r107243 && r107245;
        bool r107247 = r107240 || r107246;
        double r107248 = r107230 / r107229;
        double r107249 = r107235 / r107248;
        double r107250 = r107236 / r107230;
        double r107251 = r107247 ? r107249 : r107250;
        double r107252 = r107233 ? r107238 : r107251;
        return r107252;
}

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 z) < -1.057433920064963e+133

    1. Initial program 34.0

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

    2. Simplified16.5

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

    4. Applied associate-*r/4.0

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

    6. Applied clear-num4.1

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

    if -1.057433920064963e+133 < (/ y z) < -1.0665637347194774e-221 or 1.5828563463705101e-127 < (/ y z) < 2.5905951762285947e+176

    1. Initial program 6.8

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

    2. Simplified0.2

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

    4. Applied associate-*r/10.3

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

    6. Applied associate-/l*0.2

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

    if -1.0665637347194774e-221 < (/ y z) < 1.5828563463705101e-127 or 2.5905951762285947e+176 < (/ y z)

    1. Initial program 22.0

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

    2. Simplified12.1

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

    4. Applied associate-*r/1.2

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.057433920064963 \cdot 10^{133}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le -1.0665637347194774 \cdot 10^{-221} \lor \neg \left(\frac{y}{z} \le 1.5828563463705101 \cdot 10^{-127}\right) \land \frac{y}{z} \le 2.5905951762285947 \cdot 10^{176}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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)))