Average Error: 6.0 → 3.0
Time: 19.4s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.74920595474597988684148347386440472749 \cdot 10^{149} \lor \neg \left(z \le 6.753152462290180666397600123488286298543 \cdot 10^{153}\right):\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - y \cdot \left(\left({z}^{2} - t\right) \cdot 4\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.74920595474597988684148347386440472749 \cdot 10^{149} \lor \neg \left(z \le 6.753152462290180666397600123488286298543 \cdot 10^{153}\right):\\
\;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\

\mathbf{else}:\\
\;\;\;\;x \cdot x - y \cdot \left(\left({z}^{2} - t\right) \cdot 4\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r439592 = x;
        double r439593 = r439592 * r439592;
        double r439594 = y;
        double r439595 = 4.0;
        double r439596 = r439594 * r439595;
        double r439597 = z;
        double r439598 = r439597 * r439597;
        double r439599 = t;
        double r439600 = r439598 - r439599;
        double r439601 = r439596 * r439600;
        double r439602 = r439593 - r439601;
        return r439602;
}
↓
double f(double x, double y, double z, double t) {
        double r439603 = z;
        double r439604 = -1.74920595474598e+149;
        bool r439605 = r439603 <= r439604;
        double r439606 = 6.75315246229018e+153;
        bool r439607 = r439603 <= r439606;
        double r439608 = !r439607;
        bool r439609 = r439605 || r439608;
        double r439610 = x;
        double r439611 = r439610 * r439610;
        double r439612 = y;
        double r439613 = 4.0;
        double r439614 = r439612 * r439613;
        double r439615 = t;
        double r439616 = sqrt(r439615);
        double r439617 = r439603 + r439616;
        double r439618 = r439614 * r439617;
        double r439619 = r439603 - r439616;
        double r439620 = r439618 * r439619;
        double r439621 = r439611 - r439620;
        double r439622 = 2.0;
        double r439623 = pow(r439603, r439622);
        double r439624 = r439623 - r439615;
        double r439625 = r439624 * r439613;
        double r439626 = r439612 * r439625;
        double r439627 = r439611 - r439626;
        double r439628 = r439609 ? r439621 : r439627;
        return r439628;
}

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
Herbie3.0
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.74920595474598e+149 or 6.75315246229018e+153 < z

    1. Initial program 61.6

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

    3. Applied add-sqr-sqrt62.6

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

    4. Applied difference-of-squares62.6

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

    5. Applied associate-*r*30.5

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

    if -1.74920595474598e+149 < z < 6.75315246229018e+153

    1. Initial program 0.1

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

    3. Applied associate-*l*0.1

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

    4. Simplified0.1

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

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.74920595474597988684148347386440472749 \cdot 10^{149} \lor \neg \left(z \le 6.753152462290180666397600123488286298543 \cdot 10^{153}\right):\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - y \cdot \left(\left({z}^{2} - t\right) \cdot 4\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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))))