Average Error: 6.1 → 3.4
Time: 14.8s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 9.2841388955091973 \cdot 10^{293}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(z + \sqrt{t}\right) \cdot \left(y \cdot 4\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 9.2841388955091973 \cdot 10^{293}:\\
\;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r536950 = x;
        double r536951 = r536950 * r536950;
        double r536952 = y;
        double r536953 = 4.0;
        double r536954 = r536952 * r536953;
        double r536955 = z;
        double r536956 = r536955 * r536955;
        double r536957 = t;
        double r536958 = r536956 - r536957;
        double r536959 = r536954 * r536958;
        double r536960 = r536951 - r536959;
        return r536960;
}
↓
double f(double x, double y, double z, double t) {
        double r536961 = z;
        double r536962 = r536961 * r536961;
        double r536963 = 9.284138895509197e+293;
        bool r536964 = r536962 <= r536963;
        double r536965 = x;
        double r536966 = r536965 * r536965;
        double r536967 = y;
        double r536968 = 4.0;
        double r536969 = r536967 * r536968;
        double r536970 = t;
        double r536971 = r536962 - r536970;
        double r536972 = r536969 * r536971;
        double r536973 = r536966 - r536972;
        double r536974 = sqrt(r536970);
        double r536975 = r536961 + r536974;
        double r536976 = r536975 * r536969;
        double r536977 = r536961 - r536974;
        double r536978 = r536976 * r536977;
        double r536979 = r536966 - r536978;
        double r536980 = r536964 ? r536973 : r536979;
        return r536980;
}

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

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 9.284138895509197e+293

    1. Initial program 0.1

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

    if 9.284138895509197e+293 < (* z z)

    1. Initial program 57.7

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

    3. Applied add-sqr-sqrt60.9

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

    4. Applied difference-of-squares60.9

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

    5. Applied associate-*r*31.5

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

    6. Simplified31.5

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

  4. Final simplification3.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 9.2841388955091973 \cdot 10^{293}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(z + \sqrt{t}\right) \cdot \left(y \cdot 4\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"

  :herbie-target
  (- (* x x) (* 4.0 (* y (- (* z z) t))))

  (- (* x x) (* (* y 4.0) (- (* z z) t))))