Average Error: 5.6 → 2.9
Time: 15.5s
Precision: 64
\[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 5.86519200437255 \cdot 10^{+302}:\\ \;\;\;\;x \cdot x - \left(4.0 \cdot y\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(\sqrt{t} + z\right) \cdot \left(4.0 \cdot y\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 5.86519200437255 \cdot 10^{+302}:\\
\;\;\;\;x \cdot x - \left(4.0 \cdot y\right) \cdot \left(z \cdot z - t\right)\\

\mathbf{else}:\\
\;\;\;\;x \cdot x - \left(\left(\sqrt{t} + z\right) \cdot \left(4.0 \cdot y\right)\right) \cdot \left(z - \sqrt{t}\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r32626692 = x;
        double r32626693 = r32626692 * r32626692;
        double r32626694 = y;
        double r32626695 = 4.0;
        double r32626696 = r32626694 * r32626695;
        double r32626697 = z;
        double r32626698 = r32626697 * r32626697;
        double r32626699 = t;
        double r32626700 = r32626698 - r32626699;
        double r32626701 = r32626696 * r32626700;
        double r32626702 = r32626693 - r32626701;
        return r32626702;
}
↓
double f(double x, double y, double z, double t) {
        double r32626703 = z;
        double r32626704 = r32626703 * r32626703;
        double r32626705 = 5.86519200437255e+302;
        bool r32626706 = r32626704 <= r32626705;
        double r32626707 = x;
        double r32626708 = r32626707 * r32626707;
        double r32626709 = 4.0;
        double r32626710 = y;
        double r32626711 = r32626709 * r32626710;
        double r32626712 = t;
        double r32626713 = r32626704 - r32626712;
        double r32626714 = r32626711 * r32626713;
        double r32626715 = r32626708 - r32626714;
        double r32626716 = sqrt(r32626712);
        double r32626717 = r32626716 + r32626703;
        double r32626718 = r32626717 * r32626711;
        double r32626719 = r32626703 - r32626716;
        double r32626720 = r32626718 * r32626719;
        double r32626721 = r32626708 - r32626720;
        double r32626722 = r32626706 ? r32626715 : r32626721;
        return r32626722;
}

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

Target

Original5.6
Target5.6
Herbie2.9
\[x \cdot x - 4.0 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 5.86519200437255e+302

    1. Initial program 0.1

      \[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]

    if 5.86519200437255e+302 < (* z z)

    1. Initial program 57.9

      \[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt59.7

      \[\leadsto x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - \color{blue}{\sqrt{t} \cdot \sqrt{t}}\right)\]

    4. Applied difference-of-squares59.7

      \[\leadsto x \cdot x - \left(y \cdot 4.0\right) \cdot \color{blue}{\left(\left(z + \sqrt{t}\right) \cdot \left(z - \sqrt{t}\right)\right)}\]

    5. Applied associate-*r*29.9

      \[\leadsto x \cdot x - \color{blue}{\left(\left(y \cdot 4.0\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 5.86519200437255 \cdot 10^{+302}:\\ \;\;\;\;x \cdot x - \left(4.0 \cdot y\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(\sqrt{t} + z\right) \cdot \left(4.0 \cdot y\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"

  :herbie-target
  (- (* x x) (* 4.0 (* y (- (* z z) t))))

  (- (* x x) (* (* y 4.0) (- (* z z) t))))