Average Error: 14.9 → 0.9
Time: 1.6m
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.373126282676869801042410117321373689886 \cdot 10^{248}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.442195260190721375763336527072648974839 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 8.016173771246957431133751072912619444155 \cdot 10^{-269}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.732643683956572152079035140544113583748 \cdot 10^{175}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -3.373126282676869801042410117321373689886 \cdot 10^{248}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\mathbf{elif}\;\frac{y}{z} \le -2.442195260190721375763336527072648974839 \cdot 10^{-111}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 8.016173771246957431133751072912619444155 \cdot 10^{-269}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 1.732643683956572152079035140544113583748 \cdot 10^{175}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r57729 = x;
        double r57730 = y;
        double r57731 = z;
        double r57732 = r57730 / r57731;
        double r57733 = t;
        double r57734 = r57732 * r57733;
        double r57735 = r57734 / r57733;
        double r57736 = r57729 * r57735;
        return r57736;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r57737 = y;
        double r57738 = z;
        double r57739 = r57737 / r57738;
        double r57740 = -3.37312628267687e+248;
        bool r57741 = r57739 <= r57740;
        double r57742 = 1.0;
        double r57743 = x;
        double r57744 = r57743 * r57737;
        double r57745 = r57738 / r57744;
        double r57746 = r57742 / r57745;
        double r57747 = -2.4421952601907214e-111;
        bool r57748 = r57739 <= r57747;
        double r57749 = r57738 / r57737;
        double r57750 = r57743 / r57749;
        double r57751 = 8.016173771246957e-269;
        bool r57752 = r57739 <= r57751;
        double r57753 = r57742 / r57738;
        double r57754 = r57744 * r57753;
        double r57755 = 1.732643683956572e+175;
        bool r57756 = r57739 <= r57755;
        double r57757 = r57756 ? r57750 : r57746;
        double r57758 = r57752 ? r57754 : r57757;
        double r57759 = r57748 ? r57750 : r57758;
        double r57760 = r57741 ? r57746 : r57759;
        return r57760;
}

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) < -3.37312628267687e+248 or 1.732643683956572e+175 < (/ y z)

    1. Initial program 44.2

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

    2. Simplified1.1

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

    4. Applied clear-num1.2

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

    if -3.37312628267687e+248 < (/ y z) < -2.4421952601907214e-111 or 8.016173771246957e-269 < (/ y z) < 1.732643683956572e+175

    1. Initial program 8.5

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

    2. Simplified10.1

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

    4. Applied associate-/l*0.2

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

    if -2.4421952601907214e-111 < (/ y z) < 8.016173771246957e-269

    1. Initial program 15.9

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

    2. Simplified1.9

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

    4. Applied div-inv2.0

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.373126282676869801042410117321373689886 \cdot 10^{248}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.442195260190721375763336527072648974839 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 8.016173771246957431133751072912619444155 \cdot 10^{-269}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.732643683956572152079035140544113583748 \cdot 10^{175}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +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)))