Average Error: 14.5 → 0.7
Time: 14.2s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.0746832567059644 \cdot 10^{+132}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \mathbf{elif}\;\frac{y}{z} \le -3.2662471639158817 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 6.625650070508862 \cdot 10^{-168}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 5.643944490104231 \cdot 10^{+261}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -5.0746832567059644 \cdot 10^{+132}:\\
\;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\

\mathbf{elif}\;\frac{y}{z} \le -3.2662471639158817 \cdot 10^{-215}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 6.625650070508862 \cdot 10^{-168}:\\
\;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 5.643944490104231 \cdot 10^{+261}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r7415162 = x;
        double r7415163 = y;
        double r7415164 = z;
        double r7415165 = r7415163 / r7415164;
        double r7415166 = t;
        double r7415167 = r7415165 * r7415166;
        double r7415168 = r7415167 / r7415166;
        double r7415169 = r7415162 * r7415168;
        return r7415169;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r7415170 = y;
        double r7415171 = z;
        double r7415172 = r7415170 / r7415171;
        double r7415173 = -5.0746832567059644e+132;
        bool r7415174 = r7415172 <= r7415173;
        double r7415175 = 1.0;
        double r7415176 = x;
        double r7415177 = r7415170 * r7415176;
        double r7415178 = r7415171 / r7415177;
        double r7415179 = r7415175 / r7415178;
        double r7415180 = -3.2662471639158817e-215;
        bool r7415181 = r7415172 <= r7415180;
        double r7415182 = r7415171 / r7415170;
        double r7415183 = r7415176 / r7415182;
        double r7415184 = 6.625650070508862e-168;
        bool r7415185 = r7415172 <= r7415184;
        double r7415186 = r7415175 / r7415171;
        double r7415187 = r7415177 * r7415186;
        double r7415188 = 5.643944490104231e+261;
        bool r7415189 = r7415172 <= r7415188;
        double r7415190 = r7415176 * r7415172;
        double r7415191 = r7415189 ? r7415190 : r7415179;
        double r7415192 = r7415185 ? r7415187 : r7415191;
        double r7415193 = r7415181 ? r7415183 : r7415192;
        double r7415194 = r7415174 ? r7415179 : r7415193;
        return r7415194;
}

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 4 regimes

  2. if (/ y z) < -5.0746832567059644e+132 or 5.643944490104231e+261 < (/ y z)

    1. Initial program 34.4

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

    2. Simplified21.9

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

    3. Taylor expanded around -inf 2.7

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

    5. Applied clear-num2.8

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

    if -5.0746832567059644e+132 < (/ y z) < -3.2662471639158817e-215

    1. Initial program 7.1

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

    2. Simplified0.2

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

    3. Taylor expanded around -inf 10.0

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

    5. Applied associate-/l*0.2

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

    if -3.2662471639158817e-215 < (/ y z) < 6.625650070508862e-168

    1. Initial program 17.5

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

    2. Simplified10.2

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

    3. Taylor expanded around -inf 0.7

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

    5. Applied div-inv0.7

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

    if 6.625650070508862e-168 < (/ y z) < 5.643944490104231e+261

    1. Initial program 9.2

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

    2. Simplified0.3

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.0746832567059644 \cdot 10^{+132}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \mathbf{elif}\;\frac{y}{z} \le -3.2662471639158817 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 6.625650070508862 \cdot 10^{-168}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 5.643944490104231 \cdot 10^{+261}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019121 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))