Average Error: 14.9 → 0.8
Time: 9.2s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.336855438751845253690247898530172235276 \cdot 10^{200}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.140183350781710951892007925496689372501 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 8.498087209476109758731119739347125435518 \cdot 10^{-318}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 6.962111496293719814616574831940399431433 \cdot 10^{307}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -5.336855438751845253690247898530172235276 \cdot 10^{200}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.140183350781710951892007925496689372501 \cdot 10^{-100}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 8.498087209476109758731119739347125435518 \cdot 10^{-318}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 6.962111496293719814616574831940399431433 \cdot 10^{307}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r56825 = x;
        double r56826 = y;
        double r56827 = z;
        double r56828 = r56826 / r56827;
        double r56829 = t;
        double r56830 = r56828 * r56829;
        double r56831 = r56830 / r56829;
        double r56832 = r56825 * r56831;
        return r56832;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r56833 = y;
        double r56834 = z;
        double r56835 = r56833 / r56834;
        double r56836 = -5.336855438751845e+200;
        bool r56837 = r56835 <= r56836;
        double r56838 = x;
        double r56839 = r56838 / r56834;
        double r56840 = r56833 * r56839;
        double r56841 = -1.140183350781711e-100;
        bool r56842 = r56835 <= r56841;
        double r56843 = r56835 * r56838;
        double r56844 = 8.4980872094761e-318;
        bool r56845 = r56835 <= r56844;
        double r56846 = r56833 * r56838;
        double r56847 = r56846 / r56834;
        double r56848 = 6.96211149629372e+307;
        bool r56849 = r56835 <= r56848;
        double r56850 = r56834 / r56833;
        double r56851 = r56838 / r56850;
        double r56852 = r56849 ? r56851 : r56840;
        double r56853 = r56845 ? r56847 : r56852;
        double r56854 = r56842 ? r56843 : r56853;
        double r56855 = r56837 ? r56840 : r56854;
        return r56855;
}

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) < -5.336855438751845e+200 or 6.96211149629372e+307 < (/ y z)

    1. Initial program 46.8

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

    2. Simplified1.2

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

    4. Applied *-un-lft-identity1.2

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

    5. Applied times-frac1.2

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

    6. Simplified1.2

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

    if -5.336855438751845e+200 < (/ y z) < -1.140183350781711e-100

    1. Initial program 7.1

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

    2. Simplified10.7

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

    4. Applied associate-/l*11.0

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

    6. Applied associate-/r/0.3

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

    if -1.140183350781711e-100 < (/ y z) < 8.4980872094761e-318

    1. Initial program 16.3

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

    2. Simplified1.6

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

    if 8.4980872094761e-318 < (/ y z) < 6.96211149629372e+307

    1. Initial program 11.3

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

    2. Simplified7.6

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

    4. Applied clear-num7.9

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

    5. Simplified7.9

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{x \cdot y}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity7.9

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

    8. Applied times-frac1.0

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

    9. Applied associate-/r*0.6

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

    10. Simplified0.5

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.336855438751845253690247898530172235276 \cdot 10^{200}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.140183350781710951892007925496689372501 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 8.498087209476109758731119739347125435518 \cdot 10^{-318}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 6.962111496293719814616574831940399431433 \cdot 10^{307}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 +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)))