Average Error: 5.9 → 0.1
Time: 3.7s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\left(x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right) - \left(y \cdot 4\right) \cdot \left(-t\right)\]
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(y \cdot 4\right) \cdot \left(-t\right)
double f(double x, double y, double z, double t) {
        double r730808 = x;
        double r730809 = r730808 * r730808;
        double r730810 = y;
        double r730811 = 4.0;
        double r730812 = r730810 * r730811;
        double r730813 = z;
        double r730814 = r730813 * r730813;
        double r730815 = t;
        double r730816 = r730814 - r730815;
        double r730817 = r730812 * r730816;
        double r730818 = r730809 - r730817;
        return r730818;
}
↓
double f(double x, double y, double z, double t) {
        double r730819 = x;
        double r730820 = r730819 * r730819;
        double r730821 = z;
        double r730822 = y;
        double r730823 = 4.0;
        double r730824 = r730822 * r730823;
        double r730825 = r730821 * r730824;
        double r730826 = r730821 * r730825;
        double r730827 = r730820 - r730826;
        double r730828 = t;
        double r730829 = -r730828;
        double r730830 = r730824 * r730829;
        double r730831 = r730827 - r730830;
        return r730831;
}

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
Target5.8
Herbie0.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 5.9

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

  3. Applied sub-neg5.9

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

  4. Applied distribute-lft-in5.9

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

  5. Applied associate--r+5.9

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

  6. Simplified5.9

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

  8. Applied associate-*l*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020021 
(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))))