Average Error: 6.1 → 3.5
Time: 14.8s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 8.098576661615138715128029141599860044707 \cdot 10^{279}:\\ \;\;\;\;x \cdot x - \left(4 \cdot y\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(\sqrt{t} + z\right) \cdot \left(4 \cdot y\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 8.098576661615138715128029141599860044707 \cdot 10^{279}:\\
\;\;\;\;x \cdot x - \left(4 \cdot y\right) \cdot \left(z \cdot z - t\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r30510385 = x;
        double r30510386 = r30510385 * r30510385;
        double r30510387 = y;
        double r30510388 = 4.0;
        double r30510389 = r30510387 * r30510388;
        double r30510390 = z;
        double r30510391 = r30510390 * r30510390;
        double r30510392 = t;
        double r30510393 = r30510391 - r30510392;
        double r30510394 = r30510389 * r30510393;
        double r30510395 = r30510386 - r30510394;
        return r30510395;
}
↓
double f(double x, double y, double z, double t) {
        double r30510396 = z;
        double r30510397 = r30510396 * r30510396;
        double r30510398 = 8.098576661615139e+279;
        bool r30510399 = r30510397 <= r30510398;
        double r30510400 = x;
        double r30510401 = r30510400 * r30510400;
        double r30510402 = 4.0;
        double r30510403 = y;
        double r30510404 = r30510402 * r30510403;
        double r30510405 = t;
        double r30510406 = r30510397 - r30510405;
        double r30510407 = r30510404 * r30510406;
        double r30510408 = r30510401 - r30510407;
        double r30510409 = sqrt(r30510405);
        double r30510410 = r30510409 + r30510396;
        double r30510411 = r30510410 * r30510404;
        double r30510412 = r30510396 - r30510409;
        double r30510413 = r30510411 * r30510412;
        double r30510414 = r30510401 - r30510413;
        double r30510415 = r30510399 ? r30510408 : r30510414;
        return r30510415;
}

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
Herbie3.5
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 8.098576661615139e+279

    1. Initial program 0.1

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

    if 8.098576661615139e+279 < (* z z)

    1. Initial program 53.9

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
    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*30.1

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 8.098576661615138715128029141599860044707 \cdot 10^{279}:\\ \;\;\;\;x \cdot x - \left(4 \cdot y\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(\sqrt{t} + z\right) \cdot \left(4 \cdot y\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(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))))