Average Error: 6.1 → 3.2
Time: 4.3s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 4.572007818695644460099812881291317082403 \cdot 10^{293}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 4.572007818695644460099812881291317082403 \cdot 10^{293}:\\
\;\;\;\;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 r533828 = x;
        double r533829 = r533828 * r533828;
        double r533830 = y;
        double r533831 = 4.0;
        double r533832 = r533830 * r533831;
        double r533833 = z;
        double r533834 = r533833 * r533833;
        double r533835 = t;
        double r533836 = r533834 - r533835;
        double r533837 = r533832 * r533836;
        double r533838 = r533829 - r533837;
        return r533838;
}
↓
double f(double x, double y, double z, double t) {
        double r533839 = z;
        double r533840 = r533839 * r533839;
        double r533841 = 4.5720078186956445e+293;
        bool r533842 = r533840 <= r533841;
        double r533843 = x;
        double r533844 = r533843 * r533843;
        double r533845 = y;
        double r533846 = 4.0;
        double r533847 = r533845 * r533846;
        double r533848 = t;
        double r533849 = r533840 - r533848;
        double r533850 = r533847 * r533849;
        double r533851 = r533844 - r533850;
        double r533852 = sqrt(r533848);
        double r533853 = r533839 + r533852;
        double r533854 = r533847 * r533853;
        double r533855 = r533839 - r533852;
        double r533856 = r533854 * r533855;
        double r533857 = r533844 - r533856;
        double r533858 = r533842 ? r533851 : r533857;
        return r533858;
}

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

Original6.1
Target6.1
Herbie3.2
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 4.5720078186956445e+293

    1. Initial program 0.1

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

    if 4.5720078186956445e+293 < (* z z)

    1. Initial program 59.0

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

    3. Applied add-sqr-sqrt61.7

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

    4. Applied difference-of-squares61.7

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

    5. Applied associate-*r*30.8

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

  4. Final simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 4.572007818695644460099812881291317082403 \cdot 10^{293}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019362 
(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))))