Average Error: 5.9 → 4.3
Time: 4.6s
Precision: binary64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) = -inf.0:\\ \;\;\;\;x \cdot x + \left(y \cdot \left(4 \cdot \left(z + \sqrt{t}\right)\right)\right) \cdot \left(\sqrt{t} - z\right)\\ \mathbf{elif}\;\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \le 1.69404941835470701 \cdot 10^{302}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array}\]
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) = -inf.0:\\
\;\;\;\;x \cdot x + \left(y \cdot \left(4 \cdot \left(z + \sqrt{t}\right)\right)\right) \cdot \left(\sqrt{t} - z\right)\\

\mathbf{elif}\;\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \le 1.69404941835470701 \cdot 10^{302}:\\
\;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\

\mathbf{else}:\\
\;\;\;\;x \cdot x\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x * x)) - ((double) (((double) (y * 4.0)) * ((double) (((double) (z * z)) - t))))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((double) (((double) (y * 4.0)) * ((double) (((double) (z * z)) - t)))) <= -inf.0)) {
		VAR = ((double) (((double) (x * x)) + ((double) (((double) (y * ((double) (4.0 * ((double) (z + ((double) sqrt(t)))))))) * ((double) (((double) sqrt(t)) - z))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (y * 4.0)) * ((double) (((double) (z * z)) - t)))) <= 1.694049418354707e+302)) {
			VAR_1 = ((double) (((double) (x * x)) + ((double) (((double) (y * 4.0)) * ((double) (t - ((double) (z * z))))))));
		} else {
			VAR_1 = ((double) (x * x));
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Original5.9
Target5.9
Herbie4.3
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (* (* y 4.0) (- (* z z) t)) < -inf.0

    1. Initial program 64.0

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

    3. Applied add-sqr-sqrt64.0

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

    4. Applied difference-of-squares64.0

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

    5. Applied associate-*r*34.5

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

    6. Simplified34.2

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

    if -inf.0 < (* (* y 4.0) (- (* z z) t)) < 1.69404941835470701e302

    1. Initial program 0.1

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

    if 1.69404941835470701e302 < (* (* y 4.0) (- (* z z) t))

    1. Initial program 59.8

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

    2. Taylor expanded around 0 54.2

      \[\leadsto \color{blue}{{x}^{2}}\]

    3. Simplified54.2

      \[\leadsto \color{blue}{x \cdot x}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification4.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) = -inf.0:\\ \;\;\;\;x \cdot x + \left(y \cdot \left(4 \cdot \left(z + \sqrt{t}\right)\right)\right) \cdot \left(\sqrt{t} - z\right)\\ \mathbf{elif}\;\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \le 1.69404941835470701 \cdot 10^{302}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"
  :precision binary64

  :herbie-target
  (- (* x x) (* 4.0 (* y (- (* z z) t))))

  (- (* x x) (* (* y 4.0) (- (* z z) t))))