Average Error: 6.0 → 4.0
Time: 16.3s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 5.262792164914477010314770127344285061599 \cdot 10^{261}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 5.262792164914477010314770127344285061599 \cdot 10^{261}:\\
\;\;\;\;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 r519578 = x;
        double r519579 = r519578 * r519578;
        double r519580 = y;
        double r519581 = 4.0;
        double r519582 = r519580 * r519581;
        double r519583 = z;
        double r519584 = r519583 * r519583;
        double r519585 = t;
        double r519586 = r519584 - r519585;
        double r519587 = r519582 * r519586;
        double r519588 = r519579 - r519587;
        return r519588;
}
↓
double f(double x, double y, double z, double t) {
        double r519589 = z;
        double r519590 = r519589 * r519589;
        double r519591 = 5.262792164914477e+261;
        bool r519592 = r519590 <= r519591;
        double r519593 = x;
        double r519594 = r519593 * r519593;
        double r519595 = y;
        double r519596 = 4.0;
        double r519597 = r519595 * r519596;
        double r519598 = t;
        double r519599 = r519590 - r519598;
        double r519600 = r519597 * r519599;
        double r519601 = r519594 - r519600;
        double r519602 = sqrt(r519598);
        double r519603 = r519589 + r519602;
        double r519604 = r519597 * r519603;
        double r519605 = r519589 - r519602;
        double r519606 = r519604 * r519605;
        double r519607 = r519594 - r519606;
        double r519608 = r519592 ? r519601 : r519607;
        return r519608;
}

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
Target6.0
Herbie4.0
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 5.262792164914477e+261

    1. Initial program 0.1

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

    if 5.262792164914477e+261 < (* z z)

    1. Initial program 48.0

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

    3. Applied add-sqr-sqrt56.8

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

    4. Applied difference-of-squares56.8

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

    5. Applied associate-*r*32.3

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

  4. Final simplification4.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 5.262792164914477010314770127344285061599 \cdot 10^{261}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(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))))