Average Error: 6.0 → 0.1
Time: 12.8s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\left(x \cdot x - z \cdot \left(\left(y \cdot 4\right) \cdot z\right)\right) - \left(4 \cdot \left(-y\right)\right) \cdot t\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\left(x \cdot x - z \cdot \left(\left(y \cdot 4\right) \cdot z\right)\right) - \left(4 \cdot \left(-y\right)\right) \cdot t
double f(double x, double y, double z, double t) {
        double r30866219 = x;
        double r30866220 = r30866219 * r30866219;
        double r30866221 = y;
        double r30866222 = 4.0;
        double r30866223 = r30866221 * r30866222;
        double r30866224 = z;
        double r30866225 = r30866224 * r30866224;
        double r30866226 = t;
        double r30866227 = r30866225 - r30866226;
        double r30866228 = r30866223 * r30866227;
        double r30866229 = r30866220 - r30866228;
        return r30866229;
}
↓
double f(double x, double y, double z, double t) {
        double r30866230 = x;
        double r30866231 = r30866230 * r30866230;
        double r30866232 = z;
        double r30866233 = y;
        double r30866234 = 4.0;
        double r30866235 = r30866233 * r30866234;
        double r30866236 = r30866235 * r30866232;
        double r30866237 = r30866232 * r30866236;
        double r30866238 = r30866231 - r30866237;
        double r30866239 = -r30866233;
        double r30866240 = r30866234 * r30866239;
        double r30866241 = t;
        double r30866242 = r30866240 * r30866241;
        double r30866243 = r30866238 - r30866242;
        return r30866243;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Results

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Target

Original6.0
Target6.0
Herbie0.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

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. Applied associate--r+6.0

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

  7. Applied associate-*r*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"

  :herbie-target
  (- (* x x) (* 4.0 (* y (- (* z z) t))))

  (- (* x x) (* (* y 4.0) (- (* z z) t))))