Average Error: 5.4 → 2.9
Time: 22.5s
Precision: 64
\[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 6.3258976424500374 \cdot 10^{+289}:\\ \;\;\;\;x \cdot x - \left(4.0 \cdot y\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(\sqrt{t} + z\right) \cdot \left(4.0 \cdot y\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
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 6.3258976424500374 \cdot 10^{+289}:\\
\;\;\;\;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 r42282301 = x;
        double r42282302 = r42282301 * r42282301;
        double r42282303 = y;
        double r42282304 = 4.0;
        double r42282305 = r42282303 * r42282304;
        double r42282306 = z;
        double r42282307 = r42282306 * r42282306;
        double r42282308 = t;
        double r42282309 = r42282307 - r42282308;
        double r42282310 = r42282305 * r42282309;
        double r42282311 = r42282302 - r42282310;
        return r42282311;
}
↓
double f(double x, double y, double z, double t) {
        double r42282312 = z;
        double r42282313 = r42282312 * r42282312;
        double r42282314 = 6.3258976424500374e+289;
        bool r42282315 = r42282313 <= r42282314;
        double r42282316 = x;
        double r42282317 = r42282316 * r42282316;
        double r42282318 = 4.0;
        double r42282319 = y;
        double r42282320 = r42282318 * r42282319;
        double r42282321 = t;
        double r42282322 = r42282313 - r42282321;
        double r42282323 = r42282320 * r42282322;
        double r42282324 = r42282317 - r42282323;
        double r42282325 = sqrt(r42282321);
        double r42282326 = r42282325 + r42282312;
        double r42282327 = r42282326 * r42282320;
        double r42282328 = r42282312 - r42282325;
        double r42282329 = r42282327 * r42282328;
        double r42282330 = r42282317 - r42282329;
        double r42282331 = r42282315 ? r42282324 : r42282330;
        return r42282331;
}

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

Original5.4
Target5.4
Herbie2.9
\[x \cdot x - 4.0 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 6.3258976424500374e+289

    1. Initial program 0.1

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

    if 6.3258976424500374e+289 < (* z z)

    1. Initial program 53.0

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

    3. Applied add-sqr-sqrt57.0

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

    4. Applied difference-of-squares57.0

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

    5. Applied associate-*r*27.9

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

  4. Final simplification2.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 6.3258976424500374 \cdot 10^{+289}:\\ \;\;\;\;x \cdot x - \left(4.0 \cdot y\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(\sqrt{t} + z\right) \cdot \left(4.0 \cdot y\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(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))))