Average Error: 14.7 → 0.3
Time: 8.7s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -6.29544524415545219149038523268139908958 \cdot 10^{285}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.575588880456927846517204610144689059531 \cdot 10^{-286}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 3.757059281014894097749857788400547545613 \cdot 10^{-220}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.409130514825537046443418609777720419861 \cdot 10^{217}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -6.29544524415545219149038523268139908958 \cdot 10^{285}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.575588880456927846517204610144689059531 \cdot 10^{-286}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 3.757059281014894097749857788400547545613 \cdot 10^{-220}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 1.409130514825537046443418609777720419861 \cdot 10^{217}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r71146 = x;
        double r71147 = y;
        double r71148 = z;
        double r71149 = r71147 / r71148;
        double r71150 = t;
        double r71151 = r71149 * r71150;
        double r71152 = r71151 / r71150;
        double r71153 = r71146 * r71152;
        return r71153;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r71154 = y;
        double r71155 = z;
        double r71156 = r71154 / r71155;
        double r71157 = -6.295445244155452e+285;
        bool r71158 = r71156 <= r71157;
        double r71159 = x;
        double r71160 = r71159 * r71154;
        double r71161 = 1.0;
        double r71162 = r71161 / r71155;
        double r71163 = r71160 * r71162;
        double r71164 = -1.5755888804569278e-286;
        bool r71165 = r71156 <= r71164;
        double r71166 = r71155 / r71154;
        double r71167 = r71159 / r71166;
        double r71168 = 3.757059281014894e-220;
        bool r71169 = r71156 <= r71168;
        double r71170 = r71160 / r71155;
        double r71171 = 1.409130514825537e+217;
        bool r71172 = r71156 <= r71171;
        double r71173 = r71156 * r71159;
        double r71174 = r71159 / r71155;
        double r71175 = r71154 * r71174;
        double r71176 = r71172 ? r71173 : r71175;
        double r71177 = r71169 ? r71170 : r71176;
        double r71178 = r71165 ? r71167 : r71177;
        double r71179 = r71158 ? r71163 : r71178;
        return r71179;
}

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 5 regimes

  2. if (/ y z) < -6.295445244155452e+285

    1. Initial program 58.1

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

    2. Simplified0.2

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

    4. Applied div-inv0.3

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

    if -6.295445244155452e+285 < (/ y z) < -1.5755888804569278e-286

    1. Initial program 10.7

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

    2. Simplified7.7

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

    4. Applied associate-/l*0.2

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

    if -1.5755888804569278e-286 < (/ y z) < 3.757059281014894e-220

    1. Initial program 18.8

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

    2. Simplified0.3

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

    4. Applied associate-/l*15.6

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

    5. Taylor expanded around 0 0.3

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

    if 3.757059281014894e-220 < (/ y z) < 1.409130514825537e+217

    1. Initial program 8.1

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

    2. Simplified9.2

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

    4. Applied associate-/l*0.2

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

    6. Applied div-inv0.3

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

    7. Simplified0.2

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

    if 1.409130514825537e+217 < (/ y z)

    1. Initial program 44.0

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

    2. Simplified1.0

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

    4. Applied associate-/l*29.0

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

    5. Taylor expanded around 0 1.0

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

    6. Taylor expanded around 0 1.0

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

    7. Simplified0.4

      \[\leadsto \color{blue}{\frac{x}{z} \cdot y}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -6.29544524415545219149038523268139908958 \cdot 10^{285}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.575588880456927846517204610144689059531 \cdot 10^{-286}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 3.757059281014894097749857788400547545613 \cdot 10^{-220}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.409130514825537046443418609777720419861 \cdot 10^{217}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))