Average Error: 5.7 → 3.0
Time: 5.0s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 1.42272767568397904 \cdot 10^{302}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 1.42272767568397904 \cdot 10^{302}:\\
\;\;\;\;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 r898321 = x;
        double r898322 = r898321 * r898321;
        double r898323 = y;
        double r898324 = 4.0;
        double r898325 = r898323 * r898324;
        double r898326 = z;
        double r898327 = r898326 * r898326;
        double r898328 = t;
        double r898329 = r898327 - r898328;
        double r898330 = r898325 * r898329;
        double r898331 = r898322 - r898330;
        return r898331;
}
↓
double f(double x, double y, double z, double t) {
        double r898332 = z;
        double r898333 = r898332 * r898332;
        double r898334 = 1.422727675683979e+302;
        bool r898335 = r898333 <= r898334;
        double r898336 = x;
        double r898337 = r898336 * r898336;
        double r898338 = y;
        double r898339 = 4.0;
        double r898340 = r898338 * r898339;
        double r898341 = t;
        double r898342 = r898333 - r898341;
        double r898343 = r898340 * r898342;
        double r898344 = r898337 - r898343;
        double r898345 = sqrt(r898341);
        double r898346 = r898332 + r898345;
        double r898347 = r898340 * r898346;
        double r898348 = r898332 - r898345;
        double r898349 = r898347 * r898348;
        double r898350 = r898337 - r898349;
        double r898351 = r898335 ? r898344 : r898350;
        return r898351;
}

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

Original5.7
Target5.7
Herbie3.0
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 1.422727675683979e+302

    1. Initial program 0.1

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

    if 1.422727675683979e+302 < (* z z)

    1. Initial program 61.3

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
    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*32.1

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

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 1.42272767568397904 \cdot 10^{302}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020035 
(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))))