Average Error: 6.1 → 0.1
Time: 18.3s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\left(x \cdot x - \left(\left(y \cdot 4\right) \cdot z\right) \cdot z\right) - \left(-t\right) \cdot \left(y \cdot 4\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\left(x \cdot x - \left(\left(y \cdot 4\right) \cdot z\right) \cdot z\right) - \left(-t\right) \cdot \left(y \cdot 4\right)
double f(double x, double y, double z, double t) {
        double r403737 = x;
        double r403738 = r403737 * r403737;
        double r403739 = y;
        double r403740 = 4.0;
        double r403741 = r403739 * r403740;
        double r403742 = z;
        double r403743 = r403742 * r403742;
        double r403744 = t;
        double r403745 = r403743 - r403744;
        double r403746 = r403741 * r403745;
        double r403747 = r403738 - r403746;
        return r403747;
}
↓
double f(double x, double y, double z, double t) {
        double r403748 = x;
        double r403749 = r403748 * r403748;
        double r403750 = y;
        double r403751 = 4.0;
        double r403752 = r403750 * r403751;
        double r403753 = z;
        double r403754 = r403752 * r403753;
        double r403755 = r403754 * r403753;
        double r403756 = r403749 - r403755;
        double r403757 = t;
        double r403758 = -r403757;
        double r403759 = r403758 * r403752;
        double r403760 = r403756 - r403759;
        return r403760;
}

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

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Target

Original6.1
Target6.1
Herbie0.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 6.1

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

  3. Applied sub-neg6.1

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

  4. Applied distribute-rgt-in6.1

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

  5. Applied associate--r+6.1

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

  6. Simplified6.1

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

  8. Applied associate-*r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(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))))