Average Error: 6.0 → 4.0
Time: 15.9s
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 r604638 = x;
        double r604639 = r604638 * r604638;
        double r604640 = y;
        double r604641 = 4.0;
        double r604642 = r604640 * r604641;
        double r604643 = z;
        double r604644 = r604643 * r604643;
        double r604645 = t;
        double r604646 = r604644 - r604645;
        double r604647 = r604642 * r604646;
        double r604648 = r604639 - r604647;
        return r604648;
}
↓
double f(double x, double y, double z, double t) {
        double r604649 = z;
        double r604650 = r604649 * r604649;
        double r604651 = 5.262792164914477e+261;
        bool r604652 = r604650 <= r604651;
        double r604653 = x;
        double r604654 = r604653 * r604653;
        double r604655 = y;
        double r604656 = 4.0;
        double r604657 = r604655 * r604656;
        double r604658 = t;
        double r604659 = r604650 - r604658;
        double r604660 = r604657 * r604659;
        double r604661 = r604654 - r604660;
        double r604662 = sqrt(r604658);
        double r604663 = r604649 + r604662;
        double r604664 = r604657 * r604663;
        double r604665 = r604649 - r604662;
        double r604666 = r604664 * r604665;
        double r604667 = r604654 - r604666;
        double r604668 = r604652 ? r604661 : r604667;
        return r604668;
}

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))))