Average Error: 5.9 → 0.1
Time: 4.1s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[x \cdot x - \left(\left(\left(y \cdot 4\right) \cdot z\right) \cdot z + \left(y \cdot 4\right) \cdot \left(-t\right)\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
x \cdot x - \left(\left(\left(y \cdot 4\right) \cdot z\right) \cdot z + \left(y \cdot 4\right) \cdot \left(-t\right)\right)
double f(double x, double y, double z, double t) {
        double r711128 = x;
        double r711129 = r711128 * r711128;
        double r711130 = y;
        double r711131 = 4.0;
        double r711132 = r711130 * r711131;
        double r711133 = z;
        double r711134 = r711133 * r711133;
        double r711135 = t;
        double r711136 = r711134 - r711135;
        double r711137 = r711132 * r711136;
        double r711138 = r711129 - r711137;
        return r711138;
}
↓
double f(double x, double y, double z, double t) {
        double r711139 = x;
        double r711140 = r711139 * r711139;
        double r711141 = y;
        double r711142 = 4.0;
        double r711143 = r711141 * r711142;
        double r711144 = z;
        double r711145 = r711143 * r711144;
        double r711146 = r711145 * r711144;
        double r711147 = t;
        double r711148 = -r711147;
        double r711149 = r711143 * r711148;
        double r711150 = r711146 + r711149;
        double r711151 = r711140 - r711150;
        return r711151;
}

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
Target5.9
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. 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 simplification0.1

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

Reproduce

herbie shell --seed 2020001 
(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))))