Average Error: 5.9 → 3.1
Time: 4.3s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 2.3243118769397114 \cdot 10^{304}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 2.3243118769397114 \cdot 10^{304}:\\
\;\;\;\;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 r738635 = x;
        double r738636 = r738635 * r738635;
        double r738637 = y;
        double r738638 = 4.0;
        double r738639 = r738637 * r738638;
        double r738640 = z;
        double r738641 = r738640 * r738640;
        double r738642 = t;
        double r738643 = r738641 - r738642;
        double r738644 = r738639 * r738643;
        double r738645 = r738636 - r738644;
        return r738645;
}
↓
double f(double x, double y, double z, double t) {
        double r738646 = z;
        double r738647 = r738646 * r738646;
        double r738648 = 2.3243118769397114e+304;
        bool r738649 = r738647 <= r738648;
        double r738650 = x;
        double r738651 = r738650 * r738650;
        double r738652 = y;
        double r738653 = 4.0;
        double r738654 = r738652 * r738653;
        double r738655 = t;
        double r738656 = r738647 - r738655;
        double r738657 = r738654 * r738656;
        double r738658 = r738651 - r738657;
        double r738659 = sqrt(r738655);
        double r738660 = r738646 + r738659;
        double r738661 = r738654 * r738660;
        double r738662 = r738646 - r738659;
        double r738663 = r738661 * r738662;
        double r738664 = r738651 - r738663;
        double r738665 = r738649 ? r738658 : r738664;
        return r738665;
}

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

Original5.9
Target5.9
Herbie3.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 2.3243118769397114e+304

    1. Initial program 0.1

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

    if 2.3243118769397114e+304 < (* z z)

    1. Initial program 62.9

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

    3. Applied add-sqr-sqrt63.2

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

    4. Applied difference-of-squares63.2

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

    5. Applied associate-*r*32.4

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

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 2.3243118769397114 \cdot 10^{304}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(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))))