Average Error: 6.2 → 3.3
Time: 14.3s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 1.592242099753123976008112556096410581268 \cdot 10^{305}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 1.592242099753123976008112556096410581268 \cdot 10^{305}:\\
\;\;\;\;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 r452547 = x;
        double r452548 = r452547 * r452547;
        double r452549 = y;
        double r452550 = 4.0;
        double r452551 = r452549 * r452550;
        double r452552 = z;
        double r452553 = r452552 * r452552;
        double r452554 = t;
        double r452555 = r452553 - r452554;
        double r452556 = r452551 * r452555;
        double r452557 = r452548 - r452556;
        return r452557;
}
↓
double f(double x, double y, double z, double t) {
        double r452558 = z;
        double r452559 = r452558 * r452558;
        double r452560 = 1.592242099753124e+305;
        bool r452561 = r452559 <= r452560;
        double r452562 = x;
        double r452563 = r452562 * r452562;
        double r452564 = y;
        double r452565 = 4.0;
        double r452566 = r452564 * r452565;
        double r452567 = t;
        double r452568 = r452559 - r452567;
        double r452569 = r452566 * r452568;
        double r452570 = r452563 - r452569;
        double r452571 = sqrt(r452567);
        double r452572 = r452558 + r452571;
        double r452573 = r452566 * r452572;
        double r452574 = r452558 - r452571;
        double r452575 = r452573 * r452574;
        double r452576 = r452563 - r452575;
        double r452577 = r452561 ? r452570 : r452576;
        return r452577;
}

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

Original6.2
Target6.1
Herbie3.3
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 1.592242099753124e+305

    1. Initial program 0.1

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

    if 1.592242099753124e+305 < (* z z)

    1. Initial program 62.7

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
    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*33.5

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 1.592242099753123976008112556096410581268 \cdot 10^{305}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019291 
(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))))