Average Error: 6.0 → 3.2
Time: 4.5s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 1.8646532487958418 \cdot 10^{304}:\\ \;\;\;\;x \cdot x - y \cdot \left(4 \cdot \left(z \cdot z - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 1.8646532487958418 \cdot 10^{304}:\\
\;\;\;\;x \cdot x - y \cdot \left(4 \cdot \left(z \cdot z - t\right)\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 r715364 = x;
        double r715365 = r715364 * r715364;
        double r715366 = y;
        double r715367 = 4.0;
        double r715368 = r715366 * r715367;
        double r715369 = z;
        double r715370 = r715369 * r715369;
        double r715371 = t;
        double r715372 = r715370 - r715371;
        double r715373 = r715368 * r715372;
        double r715374 = r715365 - r715373;
        return r715374;
}
↓
double f(double x, double y, double z, double t) {
        double r715375 = z;
        double r715376 = r715375 * r715375;
        double r715377 = 1.8646532487958418e+304;
        bool r715378 = r715376 <= r715377;
        double r715379 = x;
        double r715380 = r715379 * r715379;
        double r715381 = y;
        double r715382 = 4.0;
        double r715383 = t;
        double r715384 = r715376 - r715383;
        double r715385 = r715382 * r715384;
        double r715386 = r715381 * r715385;
        double r715387 = r715380 - r715386;
        double r715388 = r715381 * r715382;
        double r715389 = sqrt(r715383);
        double r715390 = r715375 + r715389;
        double r715391 = r715388 * r715390;
        double r715392 = r715375 - r715389;
        double r715393 = r715391 * r715392;
        double r715394 = r715380 - r715393;
        double r715395 = r715378 ? r715387 : r715394;
        return r715395;
}

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

Original6.0
Target5.9
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) < 1.8646532487958418e+304

    1. Initial program 0.1

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

    3. Applied associate-*l*0.1

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

    if 1.8646532487958418e+304 < (* z z)

    1. Initial program 62.3

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

    3. Applied add-sqr-sqrt63.3

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

    4. Applied difference-of-squares63.3

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

    5. Applied associate-*r*32.8

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

  4. Final simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 1.8646532487958418 \cdot 10^{304}:\\ \;\;\;\;x \cdot x - y \cdot \left(4 \cdot \left(z \cdot z - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 
(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))))