Average Error: 14.5 → 0.3
Time: 12.7s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.2592621423955549 \cdot 10^{306}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.8557707244669514 \cdot 10^{-271}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 6.22729521642663493 \cdot 10^{-190}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 6.2094051295440155 \cdot 10^{253}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -2.2592621423955549 \cdot 10^{306}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.8557707244669514 \cdot 10^{-271}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 6.22729521642663493 \cdot 10^{-190}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 6.2094051295440155 \cdot 10^{253}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r78567 = x;
        double r78568 = y;
        double r78569 = z;
        double r78570 = r78568 / r78569;
        double r78571 = t;
        double r78572 = r78570 * r78571;
        double r78573 = r78572 / r78571;
        double r78574 = r78567 * r78573;
        return r78574;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r78575 = y;
        double r78576 = z;
        double r78577 = r78575 / r78576;
        double r78578 = -2.259262142395555e+306;
        bool r78579 = r78577 <= r78578;
        double r78580 = x;
        double r78581 = r78580 * r78575;
        double r78582 = r78581 / r78576;
        double r78583 = -1.8557707244669514e-271;
        bool r78584 = r78577 <= r78583;
        double r78585 = r78580 * r78577;
        double r78586 = 6.227295216426635e-190;
        bool r78587 = r78577 <= r78586;
        double r78588 = 1.0;
        double r78589 = r78588 / r78576;
        double r78590 = r78581 * r78589;
        double r78591 = 6.209405129544016e+253;
        bool r78592 = r78577 <= r78591;
        double r78593 = r78592 ? r78585 : r78582;
        double r78594 = r78587 ? r78590 : r78593;
        double r78595 = r78584 ? r78585 : r78594;
        double r78596 = r78579 ? r78582 : r78595;
        return r78596;
}

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) < -2.259262142395555e+306 or 6.209405129544016e+253 < (/ y z)

    1. Initial program 56.0

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

    2. Simplified49.4

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

    4. Applied add-cube-cbrt49.7

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

    5. Applied *-un-lft-identity49.7

      \[\leadsto x \cdot \frac{\color{blue}{1 \cdot y}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}\]

    6. Applied times-frac49.7

      \[\leadsto x \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}}\right)}\]

    7. Applied associate-*r*12.5

      \[\leadsto \color{blue}{\left(x \cdot \frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{y}{\sqrt[3]{z}}}\]

    8. Simplified12.5

      \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \frac{y}{\sqrt[3]{z}}\]

    9. Taylor expanded around 0 0.4

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

    if -2.259262142395555e+306 < (/ y z) < -1.8557707244669514e-271 or 6.227295216426635e-190 < (/ y z) < 6.209405129544016e+253

    1. Initial program 9.3

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

    2. Simplified0.2

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

    if -1.8557707244669514e-271 < (/ y z) < 6.227295216426635e-190

    1. Initial program 17.3

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

    2. Simplified12.1

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

    4. Applied div-inv12.2

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

    5. Applied associate-*r*0.5

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.2592621423955549 \cdot 10^{306}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.8557707244669514 \cdot 10^{-271}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 6.22729521642663493 \cdot 10^{-190}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 6.2094051295440155 \cdot 10^{253}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +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)))