Average Error: 6.0 → 3.1
Time: 15.7s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 9.176206011297462936236038733146266179758 \cdot 10^{300}:\\ \;\;\;\;x \cdot x - y \cdot \left(\left(z \cdot z - t\right) \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 9.176206011297462936236038733146266179758 \cdot 10^{300}:\\
\;\;\;\;x \cdot x - y \cdot \left(\left(z \cdot z - t\right) \cdot 4\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 r402839 = x;
        double r402840 = r402839 * r402839;
        double r402841 = y;
        double r402842 = 4.0;
        double r402843 = r402841 * r402842;
        double r402844 = z;
        double r402845 = r402844 * r402844;
        double r402846 = t;
        double r402847 = r402845 - r402846;
        double r402848 = r402843 * r402847;
        double r402849 = r402840 - r402848;
        return r402849;
}
↓
double f(double x, double y, double z, double t) {
        double r402850 = z;
        double r402851 = r402850 * r402850;
        double r402852 = 9.176206011297463e+300;
        bool r402853 = r402851 <= r402852;
        double r402854 = x;
        double r402855 = r402854 * r402854;
        double r402856 = y;
        double r402857 = t;
        double r402858 = r402851 - r402857;
        double r402859 = 4.0;
        double r402860 = r402858 * r402859;
        double r402861 = r402856 * r402860;
        double r402862 = r402855 - r402861;
        double r402863 = r402856 * r402859;
        double r402864 = sqrt(r402857);
        double r402865 = r402850 + r402864;
        double r402866 = r402863 * r402865;
        double r402867 = r402850 - r402864;
        double r402868 = r402866 * r402867;
        double r402869 = r402855 - r402868;
        double r402870 = r402853 ? r402862 : r402869;
        return r402870;
}

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

Original6.0
Target6.0
Herbie3.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 9.176206011297463e+300

    1. Initial program 0.1

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

    3. Applied associate-*l*0.1

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

    4. Simplified0.1

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

    if 9.176206011297463e+300 < (* z z)

    1. Initial program 61.5

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

    3. Applied add-sqr-sqrt62.8

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

    4. Applied difference-of-squares62.8

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

    5. Applied associate-*r*31.9

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

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 9.176206011297462936236038733146266179758 \cdot 10^{300}:\\ \;\;\;\;x \cdot x - y \cdot \left(\left(z \cdot z - t\right) \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 
(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))))