Average Error: 6.1 → 3.2
Time: 4.2s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \le -8.431246247227114555666010027949841059715 \cdot 10^{301} \lor \neg \left(\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \le 3.081305145285368706745319999636237779293 \cdot 10^{307}\right):\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \le -8.431246247227114555666010027949841059715 \cdot 10^{301} \lor \neg \left(\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \le 3.081305145285368706745319999636237779293 \cdot 10^{307}\right):\\
\;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r714266 = x;
        double r714267 = r714266 * r714266;
        double r714268 = y;
        double r714269 = 4.0;
        double r714270 = r714268 * r714269;
        double r714271 = z;
        double r714272 = r714271 * r714271;
        double r714273 = t;
        double r714274 = r714272 - r714273;
        double r714275 = r714270 * r714274;
        double r714276 = r714267 - r714275;
        return r714276;
}
↓
double f(double x, double y, double z, double t) {
        double r714277 = y;
        double r714278 = 4.0;
        double r714279 = r714277 * r714278;
        double r714280 = z;
        double r714281 = r714280 * r714280;
        double r714282 = t;
        double r714283 = r714281 - r714282;
        double r714284 = r714279 * r714283;
        double r714285 = -8.431246247227115e+301;
        bool r714286 = r714284 <= r714285;
        double r714287 = 3.0813051452853687e+307;
        bool r714288 = r714284 <= r714287;
        double r714289 = !r714288;
        bool r714290 = r714286 || r714289;
        double r714291 = x;
        double r714292 = r714291 * r714291;
        double r714293 = sqrt(r714282);
        double r714294 = r714280 + r714293;
        double r714295 = r714279 * r714294;
        double r714296 = r714280 - r714293;
        double r714297 = r714295 * r714296;
        double r714298 = r714292 - r714297;
        double r714299 = r714292 - r714284;
        double r714300 = r714290 ? r714298 : r714299;
        return r714300;
}

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
Target6.0
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 (* (* y 4.0) (- (* z z) t)) < -8.431246247227115e+301 or 3.0813051452853687e+307 < (* (* y 4.0) (- (* z z) t))

    1. Initial program 61.0

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

    3. Applied add-sqr-sqrt62.8

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

    4. Applied difference-of-squares62.8

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

    5. Applied associate-*r*32.2

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

    if -8.431246247227115e+301 < (* (* y 4.0) (- (* z z) t)) < 3.0813051452853687e+307

    1. Initial program 0.1

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \le -8.431246247227114555666010027949841059715 \cdot 10^{301} \lor \neg \left(\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \le 3.081305145285368706745319999636237779293 \cdot 10^{307}\right):\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(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))))