Average Error: 5.7 → 3.1
Time: 4.8s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot z \le 1.589486051477341092507251922628894228931 \cdot 10^{298}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \cdot z \le 1.589486051477341092507251922628894228931 \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 r696451 = x;
        double r696452 = r696451 * r696451;
        double r696453 = y;
        double r696454 = 4.0;
        double r696455 = r696453 * r696454;
        double r696456 = z;
        double r696457 = r696456 * r696456;
        double r696458 = t;
        double r696459 = r696457 - r696458;
        double r696460 = r696455 * r696459;
        double r696461 = r696452 - r696460;
        return r696461;
}
↓
double f(double x, double y, double z, double t) {
        double r696462 = z;
        double r696463 = r696462 * r696462;
        double r696464 = 1.589486051477341e+298;
        bool r696465 = r696463 <= r696464;
        double r696466 = x;
        double r696467 = r696466 * r696466;
        double r696468 = y;
        double r696469 = 4.0;
        double r696470 = r696468 * r696469;
        double r696471 = t;
        double r696472 = r696463 - r696471;
        double r696473 = r696470 * r696472;
        double r696474 = r696467 - r696473;
        double r696475 = sqrt(r696471);
        double r696476 = r696462 + r696475;
        double r696477 = r696470 * r696476;
        double r696478 = r696462 - r696475;
        double r696479 = r696477 * r696478;
        double r696480 = r696467 - r696479;
        double r696481 = r696465 ? r696474 : r696480;
        return r696481;
}

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

Original5.7
Target5.7
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) < 1.589486051477341e+298

    1. Initial program 0.1

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

    if 1.589486051477341e+298 < (* z z)

    1. Initial program 59.6

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

    3. Applied add-sqr-sqrt61.8

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

    4. Applied difference-of-squares61.8

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

    5. Applied associate-*r*32.0

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

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \le 1.589486051477341092507251922628894228931 \cdot 10^{298}:\\ \;\;\;\;x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z + \sqrt{t}\right)\right) \cdot \left(z - \sqrt{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019356 
(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))))