Average Error: 6.1 → 3.3
Time: 11.7s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 6.12322392683654523 \cdot 10^{304}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 6.12322392683654523 \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 r795966 = x;
        double r795967 = r795966 * r795966;
        double r795968 = y;
        double r795969 = 4.0;
        double r795970 = r795968 * r795969;
        double r795971 = z;
        double r795972 = r795971 * r795971;
        double r795973 = t;
        double r795974 = r795972 - r795973;
        double r795975 = r795970 * r795974;
        double r795976 = r795967 - r795975;
        return r795976;
}
↓
double f(double x, double y, double z, double t) {
        double r795977 = z;
        double r795978 = r795977 * r795977;
        double r795979 = 6.123223926836545e+304;
        bool r795980 = r795978 <= r795979;
        double r795981 = x;
        double r795982 = r795981 * r795981;
        double r795983 = y;
        double r795984 = 4.0;
        double r795985 = r795983 * r795984;
        double r795986 = t;
        double r795987 = r795978 - r795986;
        double r795988 = r795985 * r795987;
        double r795989 = r795982 - r795988;
        double r795990 = sqrt(r795986);
        double r795991 = r795977 + r795990;
        double r795992 = r795985 * r795991;
        double r795993 = r795977 - r795990;
        double r795994 = r795992 * r795993;
        double r795995 = r795982 - r795994;
        double r795996 = r795980 ? r795989 : r795995;
        return r795996;
}

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

Original6.1
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) < 6.123223926836545e+304

    1. Initial program 0.1

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

    if 6.123223926836545e+304 < (* 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-sqrt63.3

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

    4. Applied difference-of-squares63.3

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

    5. Applied associate-*r*33.7

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 6.12322392683654523 \cdot 10^{304}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))))