Average Error: 14.2 → 0.6
Time: 10.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.89968713120227716200243957970138180903 \cdot 10^{210}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.674553152877029983261934607928478862346 \cdot 10^{-163}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.288243228157504650577480569870560524088 \cdot 10^{170}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -2.89968713120227716200243957970138180903 \cdot 10^{210}:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le -2.674553152877029983261934607928478862346 \cdot 10^{-163}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le -0.0:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 1.288243228157504650577480569870560524088 \cdot 10^{170}:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r71996 = x;
        double r71997 = y;
        double r71998 = z;
        double r71999 = r71997 / r71998;
        double r72000 = t;
        double r72001 = r71999 * r72000;
        double r72002 = r72001 / r72000;
        double r72003 = r71996 * r72002;
        return r72003;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r72004 = y;
        double r72005 = z;
        double r72006 = r72004 / r72005;
        double r72007 = -2.899687131202277e+210;
        bool r72008 = r72006 <= r72007;
        double r72009 = 1.0;
        double r72010 = x;
        double r72011 = r72005 / r72010;
        double r72012 = r72011 / r72004;
        double r72013 = r72009 / r72012;
        double r72014 = -2.67455315287703e-163;
        bool r72015 = r72006 <= r72014;
        double r72016 = r72006 * r72010;
        double r72017 = -0.0;
        bool r72018 = r72006 <= r72017;
        double r72019 = r72004 * r72010;
        double r72020 = r72019 / r72005;
        double r72021 = 1.2882432281575047e+170;
        bool r72022 = r72006 <= r72021;
        double r72023 = r72009 / r72010;
        double r72024 = r72006 / r72023;
        double r72025 = r72010 / r72005;
        double r72026 = r72004 * r72025;
        double r72027 = r72022 ? r72024 : r72026;
        double r72028 = r72018 ? r72020 : r72027;
        double r72029 = r72015 ? r72016 : r72028;
        double r72030 = r72008 ? r72013 : r72029;
        return r72030;
}

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) < -2.899687131202277e+210

    1. Initial program 42.0

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

    2. Simplified0.7

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

    4. Applied associate-/l*1.1

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

    6. Applied clear-num1.2

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

    if -2.899687131202277e+210 < (/ y z) < -2.67455315287703e-163

    1. Initial program 7.5

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

    2. Simplified10.1

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

    4. Applied associate-/l*10.1

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

    6. Applied associate-/r/0.2

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

    if -2.67455315287703e-163 < (/ y z) < -0.0

    1. Initial program 16.9

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

    2. Simplified0.8

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

    if -0.0 < (/ y z) < 1.2882432281575047e+170

    1. Initial program 10.2

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

    2. Simplified7.5

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

    4. Applied associate-/l*6.7

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

    6. Applied div-inv6.7

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

    7. Applied associate-/r*3.5

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

    if 1.2882432281575047e+170 < (/ y z)

    1. Initial program 37.2

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

    2. Simplified2.2

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

    4. Applied *-un-lft-identity2.2

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

    5. Applied times-frac1.8

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

    6. Simplified1.8

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.89968713120227716200243957970138180903 \cdot 10^{210}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.674553152877029983261934607928478862346 \cdot 10^{-163}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.288243228157504650577480569870560524088 \cdot 10^{170}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 +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)))