Average Error: 6.0 → 6.0
Time: 6.9s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
double f(double x, double y, double z, double t) {
        double r559563 = x;
        double r559564 = r559563 * r559563;
        double r559565 = y;
        double r559566 = 4.0;
        double r559567 = r559565 * r559566;
        double r559568 = z;
        double r559569 = r559568 * r559568;
        double r559570 = t;
        double r559571 = r559569 - r559570;
        double r559572 = r559567 * r559571;
        double r559573 = r559564 - r559572;
        return r559573;
}
↓
double f(double x, double y, double z, double t) {
        double r559574 = x;
        double r559575 = r559574 * r559574;
        double r559576 = y;
        double r559577 = 4.0;
        double r559578 = r559576 * r559577;
        double r559579 = z;
        double r559580 = r559579 * r559579;
        double r559581 = t;
        double r559582 = r559580 - r559581;
        double r559583 = r559578 * r559582;
        double r559584 = r559575 - r559583;
        return r559584;
}

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
Herbie6.0
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 6.0

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

  3. Applied sub-neg6.0

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

  4. Applied distribute-lft-in6.0

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

  6. Applied associate-*r*0.1

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

  7. Final simplification6.0

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

Reproduce

herbie shell --seed 2019304 
(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))))