Average Error: 5.4 → 2.9
Time: 19.7s
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 r20598650 = x;
        double r20598651 = r20598650 * r20598650;
        double r20598652 = y;
        double r20598653 = 4.0;
        double r20598654 = r20598652 * r20598653;
        double r20598655 = z;
        double r20598656 = r20598655 * r20598655;
        double r20598657 = t;
        double r20598658 = r20598656 - r20598657;
        double r20598659 = r20598654 * r20598658;
        double r20598660 = r20598651 - r20598659;
        return r20598660;
}
↓
double f(double x, double y, double z, double t) {
        double r20598661 = z;
        double r20598662 = r20598661 * r20598661;
        double r20598663 = 6.3258976424500374e+289;
        bool r20598664 = r20598662 <= r20598663;
        double r20598665 = x;
        double r20598666 = r20598665 * r20598665;
        double r20598667 = 4.0;
        double r20598668 = y;
        double r20598669 = r20598667 * r20598668;
        double r20598670 = t;
        double r20598671 = r20598662 - r20598670;
        double r20598672 = r20598669 * r20598671;
        double r20598673 = r20598666 - r20598672;
        double r20598674 = sqrt(r20598670);
        double r20598675 = r20598674 + r20598661;
        double r20598676 = r20598675 * r20598669;
        double r20598677 = r20598661 - r20598674;
        double r20598678 = r20598676 * r20598677;
        double r20598679 = r20598666 - r20598678;
        double r20598680 = r20598664 ? r20598673 : r20598679;
        return r20598680;
}

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))))