Average Error: 6.2 → 0.1
Time: 10.7s
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 r640095 = x;
        double r640096 = r640095 * r640095;
        double r640097 = y;
        double r640098 = 4.0;
        double r640099 = r640097 * r640098;
        double r640100 = z;
        double r640101 = r640100 * r640100;
        double r640102 = t;
        double r640103 = r640101 - r640102;
        double r640104 = r640099 * r640103;
        double r640105 = r640096 - r640104;
        return r640105;
}
↓
double f(double x, double y, double z, double t) {
        double r640106 = x;
        double r640107 = r640106 * r640106;
        double r640108 = y;
        double r640109 = 4.0;
        double r640110 = r640108 * r640109;
        double r640111 = z;
        double r640112 = r640110 * r640111;
        double r640113 = r640112 * r640111;
        double r640114 = r640107 - r640113;
        double r640115 = t;
        double r640116 = -r640115;
        double r640117 = r640116 * r640110;
        double r640118 = r640114 - r640117;
        return r640118;
}

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

Original6.2
Target6.2
Herbie0.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 6.2

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

  3. Applied sub-neg6.2

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

  4. Applied distribute-rgt-in6.2

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

  5. Applied associate--r+6.2

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

  6. Simplified6.2

    \[\leadsto \color{blue}{\left(x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z\right)\right)} - \left(-t\right) \cdot \left(y \cdot 4\right)\]
  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 2020046 +o rules:numerics
(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))))