Average Error: 6.1 → 3.1
Time: 4.2s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 2.94628321762693042 \cdot 10^{297}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 2.94628321762693042 \cdot 10^{297}:\\
\;\;\;\;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 r679573 = x;
        double r679574 = r679573 * r679573;
        double r679575 = y;
        double r679576 = 4.0;
        double r679577 = r679575 * r679576;
        double r679578 = z;
        double r679579 = r679578 * r679578;
        double r679580 = t;
        double r679581 = r679579 - r679580;
        double r679582 = r679577 * r679581;
        double r679583 = r679574 - r679582;
        return r679583;
}
↓
double f(double x, double y, double z, double t) {
        double r679584 = z;
        double r679585 = r679584 * r679584;
        double r679586 = 2.9462832176269304e+297;
        bool r679587 = r679585 <= r679586;
        double r679588 = x;
        double r679589 = r679588 * r679588;
        double r679590 = y;
        double r679591 = 4.0;
        double r679592 = r679590 * r679591;
        double r679593 = t;
        double r679594 = r679585 - r679593;
        double r679595 = r679592 * r679594;
        double r679596 = r679589 - r679595;
        double r679597 = sqrt(r679593);
        double r679598 = r679584 + r679597;
        double r679599 = r679592 * r679598;
        double r679600 = r679584 - r679597;
        double r679601 = r679599 * r679600;
        double r679602 = r679589 - r679601;
        double r679603 = r679587 ? r679596 : r679602;
        return r679603;
}

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
Herbie3.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 2.9462832176269304e+297

    1. Initial program 0.1

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

    if 2.9462832176269304e+297 < (* z z)

    1. Initial program 59.8

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

    3. Applied add-sqr-sqrt62.0

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

    4. Applied difference-of-squares62.0

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

    5. Applied associate-*r*29.8

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

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 2.94628321762693042 \cdot 10^{297}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(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))))