Average Error: 6.0 → 3.0
Time: 17.4s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.74920595474597988684148347386440472749 \cdot 10^{149} \lor \neg \left(z \le 6.753152462290180666397600123488286298543 \cdot 10^{153}\right):\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - y \cdot \left(\left({z}^{2} - t\right) \cdot 4\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.74920595474597988684148347386440472749 \cdot 10^{149} \lor \neg \left(z \le 6.753152462290180666397600123488286298543 \cdot 10^{153}\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 - y \cdot \left(\left({z}^{2} - t\right) \cdot 4\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r417276 = x;
        double r417277 = r417276 * r417276;
        double r417278 = y;
        double r417279 = 4.0;
        double r417280 = r417278 * r417279;
        double r417281 = z;
        double r417282 = r417281 * r417281;
        double r417283 = t;
        double r417284 = r417282 - r417283;
        double r417285 = r417280 * r417284;
        double r417286 = r417277 - r417285;
        return r417286;
}
↓
double f(double x, double y, double z, double t) {
        double r417287 = z;
        double r417288 = -1.74920595474598e+149;
        bool r417289 = r417287 <= r417288;
        double r417290 = 6.75315246229018e+153;
        bool r417291 = r417287 <= r417290;
        double r417292 = !r417291;
        bool r417293 = r417289 || r417292;
        double r417294 = x;
        double r417295 = r417294 * r417294;
        double r417296 = y;
        double r417297 = 4.0;
        double r417298 = r417296 * r417297;
        double r417299 = t;
        double r417300 = sqrt(r417299);
        double r417301 = r417287 + r417300;
        double r417302 = r417298 * r417301;
        double r417303 = r417287 - r417300;
        double r417304 = r417302 * r417303;
        double r417305 = r417295 - r417304;
        double r417306 = 2.0;
        double r417307 = pow(r417287, r417306);
        double r417308 = r417307 - r417299;
        double r417309 = r417308 * r417297;
        double r417310 = r417296 * r417309;
        double r417311 = r417295 - r417310;
        double r417312 = r417293 ? r417305 : r417311;
        return r417312;
}

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
Herbie3.0
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.74920595474598e+149 or 6.75315246229018e+153 < z

    1. Initial program 61.6

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

    3. Applied add-sqr-sqrt62.6

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

    4. Applied difference-of-squares62.6

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

    5. Applied associate-*r*30.5

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

    if -1.74920595474598e+149 < z < 6.75315246229018e+153

    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

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

    4. Simplified0.1

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

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.74920595474597988684148347386440472749 \cdot 10^{149} \lor \neg \left(z \le 6.753152462290180666397600123488286298543 \cdot 10^{153}\right):\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - y \cdot \left(\left({z}^{2} - t\right) \cdot 4\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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))))