Average Error: 6.1 → 3.5
Time: 4.6s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 2.19138132073588015 \cdot 10^{282}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 2.19138132073588015 \cdot 10^{282}:\\
\;\;\;\;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 r657419 = x;
        double r657420 = r657419 * r657419;
        double r657421 = y;
        double r657422 = 4.0;
        double r657423 = r657421 * r657422;
        double r657424 = z;
        double r657425 = r657424 * r657424;
        double r657426 = t;
        double r657427 = r657425 - r657426;
        double r657428 = r657423 * r657427;
        double r657429 = r657420 - r657428;
        return r657429;
}
↓
double f(double x, double y, double z, double t) {
        double r657430 = z;
        double r657431 = r657430 * r657430;
        double r657432 = 2.1913813207358801e+282;
        bool r657433 = r657431 <= r657432;
        double r657434 = x;
        double r657435 = r657434 * r657434;
        double r657436 = y;
        double r657437 = 4.0;
        double r657438 = r657436 * r657437;
        double r657439 = t;
        double r657440 = r657431 - r657439;
        double r657441 = r657438 * r657440;
        double r657442 = r657435 - r657441;
        double r657443 = sqrt(r657439);
        double r657444 = r657430 + r657443;
        double r657445 = r657438 * r657444;
        double r657446 = r657430 - r657443;
        double r657447 = r657445 * r657446;
        double r657448 = r657435 - r657447;
        double r657449 = r657433 ? r657442 : r657448;
        return r657449;
}

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
Herbie3.5
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 2.1913813207358801e+282

    1. Initial program 0.1

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

    if 2.1913813207358801e+282 < (* z z)

    1. Initial program 56.0

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

    3. Applied add-sqr-sqrt60.0

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

    4. Applied difference-of-squares60.0

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

    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 simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 2.19138132073588015 \cdot 10^{282}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020083 
(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))))