Average Error: 6.1 → 0.1
Time: 3.6s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\left(x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right) - \left(-t\right) \cdot \left(y \cdot 4\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\left(x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right) - \left(-t\right) \cdot \left(y \cdot 4\right)
double f(double x, double y, double z, double t) {
        double r477796 = x;
        double r477797 = r477796 * r477796;
        double r477798 = y;
        double r477799 = 4.0;
        double r477800 = r477798 * r477799;
        double r477801 = z;
        double r477802 = r477801 * r477801;
        double r477803 = t;
        double r477804 = r477802 - r477803;
        double r477805 = r477800 * r477804;
        double r477806 = r477797 - r477805;
        return r477806;
}
↓
double f(double x, double y, double z, double t) {
        double r477807 = x;
        double r477808 = r477807 * r477807;
        double r477809 = z;
        double r477810 = y;
        double r477811 = 4.0;
        double r477812 = r477810 * r477811;
        double r477813 = r477809 * r477812;
        double r477814 = r477809 * r477813;
        double r477815 = r477808 - r477814;
        double r477816 = t;
        double r477817 = -r477816;
        double r477818 = r477817 * r477812;
        double r477819 = r477815 - r477818;
        return r477819;
}

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

Original6.1
Target6.0
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. Using strategy rm

  7. Applied associate-*l*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020003 
(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))))