Average Error: 6.2 → 3.2
Time: 4.9s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 1.521145199433776357765735930876915790283 \cdot 10^{298}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 1.521145199433776357765735930876915790283 \cdot 10^{298}:\\
\;\;\;\;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 r923389 = x;
        double r923390 = r923389 * r923389;
        double r923391 = y;
        double r923392 = 4.0;
        double r923393 = r923391 * r923392;
        double r923394 = z;
        double r923395 = r923394 * r923394;
        double r923396 = t;
        double r923397 = r923395 - r923396;
        double r923398 = r923393 * r923397;
        double r923399 = r923390 - r923398;
        return r923399;
}
↓
double f(double x, double y, double z, double t) {
        double r923400 = z;
        double r923401 = r923400 * r923400;
        double r923402 = 1.5211451994337764e+298;
        bool r923403 = r923401 <= r923402;
        double r923404 = x;
        double r923405 = r923404 * r923404;
        double r923406 = y;
        double r923407 = 4.0;
        double r923408 = r923406 * r923407;
        double r923409 = t;
        double r923410 = r923401 - r923409;
        double r923411 = r923408 * r923410;
        double r923412 = r923405 - r923411;
        double r923413 = sqrt(r923409);
        double r923414 = r923400 + r923413;
        double r923415 = r923408 * r923414;
        double r923416 = r923400 - r923413;
        double r923417 = r923415 * r923416;
        double r923418 = r923405 - r923417;
        double r923419 = r923403 ? r923412 : r923418;
        return r923419;
}

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

Original6.2
Target6.2
Herbie3.2
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 1.5211451994337764e+298

    1. Initial program 0.1

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

    if 1.5211451994337764e+298 < (* z z)

    1. Initial program 60.7

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

    3. Applied add-sqr-sqrt62.4

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

    4. Applied difference-of-squares62.4

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

    5. Applied associate-*r*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 simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 1.521145199433776357765735930876915790283 \cdot 10^{298}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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))))