Average Error: 5.6 → 3.0
Time: 20.1s
Precision: 64
\[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 1.0358464634815686 \cdot 10^{+308}:\\ \;\;\;\;x \cdot x - \left(4.0 \cdot y\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(\sqrt{t} + z\right) \cdot \left(4.0 \cdot y\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
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 1.0358464634815686 \cdot 10^{+308}:\\
\;\;\;\;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 r33543745 = x;
        double r33543746 = r33543745 * r33543745;
        double r33543747 = y;
        double r33543748 = 4.0;
        double r33543749 = r33543747 * r33543748;
        double r33543750 = z;
        double r33543751 = r33543750 * r33543750;
        double r33543752 = t;
        double r33543753 = r33543751 - r33543752;
        double r33543754 = r33543749 * r33543753;
        double r33543755 = r33543746 - r33543754;
        return r33543755;
}
↓
double f(double x, double y, double z, double t) {
        double r33543756 = z;
        double r33543757 = r33543756 * r33543756;
        double r33543758 = 1.0358464634815686e+308;
        bool r33543759 = r33543757 <= r33543758;
        double r33543760 = x;
        double r33543761 = r33543760 * r33543760;
        double r33543762 = 4.0;
        double r33543763 = y;
        double r33543764 = r33543762 * r33543763;
        double r33543765 = t;
        double r33543766 = r33543757 - r33543765;
        double r33543767 = r33543764 * r33543766;
        double r33543768 = r33543761 - r33543767;
        double r33543769 = sqrt(r33543765);
        double r33543770 = r33543769 + r33543756;
        double r33543771 = r33543770 * r33543764;
        double r33543772 = r33543756 - r33543769;
        double r33543773 = r33543771 * r33543772;
        double r33543774 = r33543761 - r33543773;
        double r33543775 = r33543759 ? r33543768 : r33543774;
        return r33543775;
}

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
Target5.5
Herbie3.0
\[x \cdot x - 4.0 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 1.0358464634815686e+308

    1. Initial program 0.1

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

    if 1.0358464634815686e+308 < (* z z)

    1. Initial program 59.8

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

    3. Applied add-sqr-sqrt60.7

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

    4. Applied difference-of-squares60.7

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

    5. Applied associate-*r*31.4

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

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 1.0358464634815686 \cdot 10^{+308}:\\ \;\;\;\;x \cdot x - \left(4.0 \cdot y\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(\sqrt{t} + z\right) \cdot \left(4.0 \cdot y\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(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))))