Average Error: 6.0 → 3.1
Time: 4.7s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 1.33207297841188052 \cdot 10^{300}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 1.33207297841188052 \cdot 10^{300}:\\
\;\;\;\;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 r785329 = x;
        double r785330 = r785329 * r785329;
        double r785331 = y;
        double r785332 = 4.0;
        double r785333 = r785331 * r785332;
        double r785334 = z;
        double r785335 = r785334 * r785334;
        double r785336 = t;
        double r785337 = r785335 - r785336;
        double r785338 = r785333 * r785337;
        double r785339 = r785330 - r785338;
        return r785339;
}
↓
double f(double x, double y, double z, double t) {
        double r785340 = z;
        double r785341 = r785340 * r785340;
        double r785342 = 1.3320729784118805e+300;
        bool r785343 = r785341 <= r785342;
        double r785344 = x;
        double r785345 = r785344 * r785344;
        double r785346 = y;
        double r785347 = 4.0;
        double r785348 = r785346 * r785347;
        double r785349 = t;
        double r785350 = r785341 - r785349;
        double r785351 = r785348 * r785350;
        double r785352 = r785345 - r785351;
        double r785353 = sqrt(r785349);
        double r785354 = r785340 + r785353;
        double r785355 = r785348 * r785354;
        double r785356 = r785340 - r785353;
        double r785357 = r785355 * r785356;
        double r785358 = r785345 - r785357;
        double r785359 = r785343 ? r785352 : r785358;
        return r785359;
}

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
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) < 1.3320729784118805e+300

    1. Initial program 0.1

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

    if 1.3320729784118805e+300 < (* z z)

    1. Initial program 61.2

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

    3. Applied add-sqr-sqrt62.7

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

    4. Applied difference-of-squares62.7

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

    5. Applied associate-*r*31.7

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

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 1.33207297841188052 \cdot 10^{300}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 
(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))))