Average Error: 6.3 → 4.1
Time: 16.0s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 4.052108237063258146574851851160968341006 \cdot 10^{262}:\\ \;\;\;\;x \cdot x - \left(\left(z \cdot z - t\right) \cdot 4\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(4 \cdot y\right) \cdot \left(\sqrt{t} + z\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 4.052108237063258146574851851160968341006 \cdot 10^{262}:\\
\;\;\;\;x \cdot x - \left(\left(z \cdot z - t\right) \cdot 4\right) \cdot y\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r33226540 = x;
        double r33226541 = r33226540 * r33226540;
        double r33226542 = y;
        double r33226543 = 4.0;
        double r33226544 = r33226542 * r33226543;
        double r33226545 = z;
        double r33226546 = r33226545 * r33226545;
        double r33226547 = t;
        double r33226548 = r33226546 - r33226547;
        double r33226549 = r33226544 * r33226548;
        double r33226550 = r33226541 - r33226549;
        return r33226550;
}
↓
double f(double x, double y, double z, double t) {
        double r33226551 = z;
        double r33226552 = r33226551 * r33226551;
        double r33226553 = 4.052108237063258e+262;
        bool r33226554 = r33226552 <= r33226553;
        double r33226555 = x;
        double r33226556 = r33226555 * r33226555;
        double r33226557 = t;
        double r33226558 = r33226552 - r33226557;
        double r33226559 = 4.0;
        double r33226560 = r33226558 * r33226559;
        double r33226561 = y;
        double r33226562 = r33226560 * r33226561;
        double r33226563 = r33226556 - r33226562;
        double r33226564 = r33226559 * r33226561;
        double r33226565 = sqrt(r33226557);
        double r33226566 = r33226565 + r33226551;
        double r33226567 = r33226564 * r33226566;
        double r33226568 = r33226551 - r33226565;
        double r33226569 = r33226567 * r33226568;
        double r33226570 = r33226556 - r33226569;
        double r33226571 = r33226554 ? r33226563 : r33226570;
        return r33226571;
}

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

Original6.3
Target6.3
Herbie4.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 4.052108237063258e+262

    1. Initial program 0.1

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

    3. Applied associate-*l*0.1

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

    if 4.052108237063258e+262 < (* z z)

    1. Initial program 49.1

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

    3. Applied add-sqr-sqrt56.5

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

    4. Applied difference-of-squares56.5

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

    5. Applied associate-*r*31.3

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

  4. Final simplification4.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 4.052108237063258146574851851160968341006 \cdot 10^{262}:\\ \;\;\;\;x \cdot x - \left(\left(z \cdot z - t\right) \cdot 4\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(4 \cdot y\right) \cdot \left(\sqrt{t} + z\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(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))))