Average Error: 6.0 → 3.3
Time: 4.3s
Precision: binary64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.68943455103201443 \cdot 10^{153} \lor \neg \left(z \le 1.3840931885894595 \cdot 10^{135}\right):\\ \;\;\;\;x \cdot x + \left(y \cdot \left(4 \cdot \left(z + \sqrt{t}\right)\right)\right) \cdot \left(\sqrt{t} - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + \left(y \cdot \left(4 \cdot t\right) - y \cdot \left(4 \cdot \left(z \cdot z\right)\right)\right)\\ \end{array}\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\begin{array}{l}
\mathbf{if}\;z \le -6.68943455103201443 \cdot 10^{153} \lor \neg \left(z \le 1.3840931885894595 \cdot 10^{135}\right):\\
\;\;\;\;x \cdot x + \left(y \cdot \left(4 \cdot \left(z + \sqrt{t}\right)\right)\right) \cdot \left(\sqrt{t} - z\right)\\

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

\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 (((z <= -6.6894345510320144e+153) || !(z <= 1.3840931885894595e+135))) {
		VAR = ((double) (((double) (x * x)) + ((double) (((double) (y * ((double) (4.0 * ((double) (z + ((double) sqrt(t)))))))) * ((double) (((double) sqrt(t)) - z))))));
	} else {
		VAR = ((double) (((double) (x * x)) + ((double) (((double) (y * ((double) (4.0 * t)))) - ((double) (y * ((double) (4.0 * ((double) (z * z))))))))));
	}
	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

Original6.0
Target6.0
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 < -6.68943455103201443e153 or 1.3840931885894595e135 < z

    1. Initial program 55.8

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

    3. Applied add-sqr-sqrt58.8

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

    4. Applied difference-of-squares58.8

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

    5. Applied associate-*r*30.8

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

    6. Simplified30.8

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

    if -6.68943455103201443e153 < z < 1.3840931885894595e135

    1. Initial program 0.1

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

    2. Simplified0.1

      \[\leadsto \color{blue}{x \cdot x + y \cdot \left(4 \cdot \left(t - z \cdot z\right)\right)}\]
    3. Using strategy rm

    4. Applied sub-neg0.1

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

    5. Applied distribute-lft-in0.1

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

    6. Applied distribute-lft-in0.1

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

    7. Simplified0.1

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.68943455103201443 \cdot 10^{153} \lor \neg \left(z \le 1.3840931885894595 \cdot 10^{135}\right):\\ \;\;\;\;x \cdot x + \left(y \cdot \left(4 \cdot \left(z + \sqrt{t}\right)\right)\right) \cdot \left(\sqrt{t} - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + \left(y \cdot \left(4 \cdot t\right) - y \cdot \left(4 \cdot \left(z \cdot z\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))))