Average Error: 6.1 → 3.3
Time: 4.6s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 5.6499424326614904 \cdot 10^{293}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 5.6499424326614904 \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 r759147 = x;
        double r759148 = r759147 * r759147;
        double r759149 = y;
        double r759150 = 4.0;
        double r759151 = r759149 * r759150;
        double r759152 = z;
        double r759153 = r759152 * r759152;
        double r759154 = t;
        double r759155 = r759153 - r759154;
        double r759156 = r759151 * r759155;
        double r759157 = r759148 - r759156;
        return r759157;
}
↓
double f(double x, double y, double z, double t) {
        double r759158 = z;
        double r759159 = r759158 * r759158;
        double r759160 = 5.6499424326614904e+293;
        bool r759161 = r759159 <= r759160;
        double r759162 = x;
        double r759163 = r759162 * r759162;
        double r759164 = y;
        double r759165 = 4.0;
        double r759166 = r759164 * r759165;
        double r759167 = t;
        double r759168 = r759159 - r759167;
        double r759169 = r759166 * r759168;
        double r759170 = r759163 - r759169;
        double r759171 = sqrt(r759167);
        double r759172 = r759158 + r759171;
        double r759173 = r759166 * r759172;
        double r759174 = r759158 - r759171;
        double r759175 = r759173 * r759174;
        double r759176 = r759163 - r759175;
        double r759177 = r759161 ? r759170 : r759176;
        return r759177;
}

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
Herbie3.3
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 5.6499424326614904e+293

    1. Initial program 0.1

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

    if 5.6499424326614904e+293 < (* z z)

    1. Initial program 59.7

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

    3. Applied add-sqr-sqrt62.0

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

    4. Applied difference-of-squares62.0

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

    5. Applied associate-*r*31.7

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 5.6499424326614904 \cdot 10^{293}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(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))))