Average Error: 6.1 → 3.9
Time: 4.0s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 1.2800532743869097 \cdot 10^{275}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 1.2800532743869097 \cdot 10^{275}:\\
\;\;\;\;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 r596160 = x;
        double r596161 = r596160 * r596160;
        double r596162 = y;
        double r596163 = 4.0;
        double r596164 = r596162 * r596163;
        double r596165 = z;
        double r596166 = r596165 * r596165;
        double r596167 = t;
        double r596168 = r596166 - r596167;
        double r596169 = r596164 * r596168;
        double r596170 = r596161 - r596169;
        return r596170;
}
↓
double f(double x, double y, double z, double t) {
        double r596171 = z;
        double r596172 = r596171 * r596171;
        double r596173 = 1.2800532743869097e+275;
        bool r596174 = r596172 <= r596173;
        double r596175 = x;
        double r596176 = r596175 * r596175;
        double r596177 = y;
        double r596178 = 4.0;
        double r596179 = r596177 * r596178;
        double r596180 = t;
        double r596181 = r596172 - r596180;
        double r596182 = r596179 * r596181;
        double r596183 = r596176 - r596182;
        double r596184 = sqrt(r596180);
        double r596185 = r596171 + r596184;
        double r596186 = r596179 * r596185;
        double r596187 = r596171 - r596184;
        double r596188 = r596186 * r596187;
        double r596189 = r596176 - r596188;
        double r596190 = r596174 ? r596183 : r596189;
        return r596190;
}

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
Herbie3.9
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 1.2800532743869097e+275

    1. Initial program 0.1

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

    if 1.2800532743869097e+275 < (* z z)

    1. Initial program 52.0

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

    3. Applied add-sqr-sqrt58.4

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

    4. Applied difference-of-squares58.4

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

    5. Applied associate-*r*32.9

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

  4. Final simplification3.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 1.2800532743869097 \cdot 10^{275}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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))))