Average Error: 5.9 → 3.6
Time: 4.9s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 8.4058266113122735 \cdot 10^{287}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 8.4058266113122735 \cdot 10^{287}:\\
\;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\

\mathbf{else}:\\
\;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r603988 = x;
        double r603989 = r603988 * r603988;
        double r603990 = y;
        double r603991 = 4.0;
        double r603992 = r603990 * r603991;
        double r603993 = z;
        double r603994 = r603993 * r603993;
        double r603995 = t;
        double r603996 = r603994 - r603995;
        double r603997 = r603992 * r603996;
        double r603998 = r603989 - r603997;
        return r603998;
}
↓
double f(double x, double y, double z, double t) {
        double r603999 = z;
        double r604000 = r603999 * r603999;
        double r604001 = 8.405826611312274e+287;
        bool r604002 = r604000 <= r604001;
        double r604003 = x;
        double r604004 = r604003 * r604003;
        double r604005 = y;
        double r604006 = 4.0;
        double r604007 = r604005 * r604006;
        double r604008 = t;
        double r604009 = r604000 - r604008;
        double r604010 = r604007 * r604009;
        double r604011 = r604004 - r604010;
        double r604012 = sqrt(r604008);
        double r604013 = r603999 + r604012;
        double r604014 = r604007 * r604013;
        double r604015 = r603999 - r604012;
        double r604016 = r604014 * r604015;
        double r604017 = r604004 - r604016;
        double r604018 = r604002 ? r604011 : r604017;
        return r604018;
}

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

Original5.9
Target5.8
Herbie3.6
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 8.405826611312274e+287

    1. Initial program 0.1

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]

    if 8.405826611312274e+287 < (* z z)

    1. Initial program 56.5

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt59.6

      \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - \color{blue}{\sqrt{t} \cdot \sqrt{t}}\right)\]

    4. Applied difference-of-squares59.6

      \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(\left(z + \sqrt{t}\right) \cdot \left(z - \sqrt{t}\right)\right)}\]

    5. Applied associate-*r*34.1

      \[\leadsto x \cdot x - \color{blue}{\left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 8.4058266113122735 \cdot 10^{287}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"
  :precision binary64

  :herbie-target
  (- (* x x) (* 4 (* y (- (* z z) t))))

  (- (* x x) (* (* y 4) (- (* z z) t))))