Average Error: 6.0 → 4.0
Time: 12.3s
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 r430107 = x;
        double r430108 = r430107 * r430107;
        double r430109 = y;
        double r430110 = 4.0;
        double r430111 = r430109 * r430110;
        double r430112 = z;
        double r430113 = r430112 * r430112;
        double r430114 = t;
        double r430115 = r430113 - r430114;
        double r430116 = r430111 * r430115;
        double r430117 = r430108 - r430116;
        return r430117;
}
↓
double f(double x, double y, double z, double t) {
        double r430118 = z;
        double r430119 = r430118 * r430118;
        double r430120 = 5.262792164914477e+261;
        bool r430121 = r430119 <= r430120;
        double r430122 = x;
        double r430123 = r430122 * r430122;
        double r430124 = y;
        double r430125 = 4.0;
        double r430126 = r430124 * r430125;
        double r430127 = t;
        double r430128 = r430119 - r430127;
        double r430129 = r430126 * r430128;
        double r430130 = r430123 - r430129;
        double r430131 = sqrt(r430127);
        double r430132 = r430118 + r430131;
        double r430133 = r430126 * r430132;
        double r430134 = r430118 - r430131;
        double r430135 = r430133 * r430134;
        double r430136 = r430123 - r430135;
        double r430137 = r430121 ? r430130 : r430136;
        return r430137;
}

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))))