Average Error: 6.2 → 3.2
Time: 4.6s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 1.521145199433776357765735930876915790283 \cdot 10^{298}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 1.521145199433776357765735930876915790283 \cdot 10^{298}:\\
\;\;\;\;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 r750146 = x;
        double r750147 = r750146 * r750146;
        double r750148 = y;
        double r750149 = 4.0;
        double r750150 = r750148 * r750149;
        double r750151 = z;
        double r750152 = r750151 * r750151;
        double r750153 = t;
        double r750154 = r750152 - r750153;
        double r750155 = r750150 * r750154;
        double r750156 = r750147 - r750155;
        return r750156;
}
↓
double f(double x, double y, double z, double t) {
        double r750157 = z;
        double r750158 = r750157 * r750157;
        double r750159 = 1.5211451994337764e+298;
        bool r750160 = r750158 <= r750159;
        double r750161 = x;
        double r750162 = r750161 * r750161;
        double r750163 = y;
        double r750164 = 4.0;
        double r750165 = r750163 * r750164;
        double r750166 = t;
        double r750167 = r750158 - r750166;
        double r750168 = r750165 * r750167;
        double r750169 = r750162 - r750168;
        double r750170 = sqrt(r750166);
        double r750171 = r750157 + r750170;
        double r750172 = r750165 * r750171;
        double r750173 = r750157 - r750170;
        double r750174 = r750172 * r750173;
        double r750175 = r750162 - r750174;
        double r750176 = r750160 ? r750169 : r750175;
        return r750176;
}

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

Original6.2
Target6.2
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) < 1.5211451994337764e+298

    1. Initial program 0.1

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

    if 1.5211451994337764e+298 < (* z z)

    1. Initial program 60.7

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

    3. Applied add-sqr-sqrt62.4

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

    4. Applied difference-of-squares62.4

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

    5. Applied associate-*r*31.3

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

  4. Final simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 1.521145199433776357765735930876915790283 \cdot 10^{298}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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))))