Average Error: 14.7 → 3.3
Time: 17.1s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.245947516265854964311200045000519905686 \cdot 10^{-233}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 6.872941476643587911784112841004328702772 \cdot 10^{-272}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.245947516265854964311200045000519905686 \cdot 10^{-233}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 6.872941476643587911784112841004328702772 \cdot 10^{-272}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r4334428 = x;
        double r4334429 = y;
        double r4334430 = z;
        double r4334431 = r4334429 / r4334430;
        double r4334432 = t;
        double r4334433 = r4334431 * r4334432;
        double r4334434 = r4334433 / r4334432;
        double r4334435 = r4334428 * r4334434;
        return r4334435;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r4334436 = y;
        double r4334437 = z;
        double r4334438 = r4334436 / r4334437;
        double r4334439 = -1.245947516265855e-233;
        bool r4334440 = r4334438 <= r4334439;
        double r4334441 = x;
        double r4334442 = r4334438 * r4334441;
        double r4334443 = 6.872941476643588e-272;
        bool r4334444 = r4334438 <= r4334443;
        double r4334445 = r4334441 * r4334436;
        double r4334446 = r4334445 / r4334437;
        double r4334447 = r4334437 / r4334436;
        double r4334448 = r4334441 / r4334447;
        double r4334449 = r4334444 ? r4334446 : r4334448;
        double r4334450 = r4334440 ? r4334442 : r4334449;
        return r4334450;
}

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) < -1.245947516265855e-233

    1. Initial program 13.3

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

    2. Simplified7.8

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

    4. Applied *-un-lft-identity7.8

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

    5. Applied times-frac4.3

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

    6. Simplified4.3

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

    if -1.245947516265855e-233 < (/ y z) < 6.872941476643588e-272

    1. Initial program 18.6

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

    2. Simplified0.4

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

    4. Applied add-cube-cbrt0.8

      \[\leadsto \frac{x \cdot y}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    5. Applied times-frac3.1

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

    7. Applied frac-times0.8

      \[\leadsto \color{blue}{\frac{x \cdot y}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    8. Simplified0.4

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

    if 6.872941476643588e-272 < (/ y z)

    1. Initial program 14.0

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

    2. Simplified8.0

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

    4. Applied associate-/l*3.8

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.245947516265854964311200045000519905686 \cdot 10^{-233}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 6.872941476643587911784112841004328702772 \cdot 10^{-272}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))