Average Error: 6.2 → 3.3
Time: 21.1s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 8.492390771886926299590046168507855606141 \cdot 10^{288}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 8.492390771886926299590046168507855606141 \cdot 10^{288}:\\
\;\;\;\;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 r401514 = x;
        double r401515 = r401514 * r401514;
        double r401516 = y;
        double r401517 = 4.0;
        double r401518 = r401516 * r401517;
        double r401519 = z;
        double r401520 = r401519 * r401519;
        double r401521 = t;
        double r401522 = r401520 - r401521;
        double r401523 = r401518 * r401522;
        double r401524 = r401515 - r401523;
        return r401524;
}
↓
double f(double x, double y, double z, double t) {
        double r401525 = z;
        double r401526 = r401525 * r401525;
        double r401527 = 8.492390771886926e+288;
        bool r401528 = r401526 <= r401527;
        double r401529 = x;
        double r401530 = r401529 * r401529;
        double r401531 = y;
        double r401532 = 4.0;
        double r401533 = r401531 * r401532;
        double r401534 = t;
        double r401535 = r401526 - r401534;
        double r401536 = r401533 * r401535;
        double r401537 = r401530 - r401536;
        double r401538 = sqrt(r401534);
        double r401539 = r401525 + r401538;
        double r401540 = r401533 * r401539;
        double r401541 = r401525 - r401538;
        double r401542 = r401540 * r401541;
        double r401543 = r401530 - r401542;
        double r401544 = r401528 ? r401537 : r401543;
        return r401544;
}

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
Herbie3.3
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* z z) < 8.492390771886926e+288

    1. Initial program 0.1

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

    if 8.492390771886926e+288 < (* z z)

    1. Initial program 56.1

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

    3. Applied add-sqr-sqrt59.7

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

    4. Applied difference-of-squares59.7

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

    5. Applied associate-*r*29.4

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 8.492390771886926299590046168507855606141 \cdot 10^{288}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(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))))