Average Error: 6.3 → 0.1
Time: 15.6s
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 r436212 = x;
        double r436213 = r436212 * r436212;
        double r436214 = y;
        double r436215 = 4.0;
        double r436216 = r436214 * r436215;
        double r436217 = z;
        double r436218 = r436217 * r436217;
        double r436219 = t;
        double r436220 = r436218 - r436219;
        double r436221 = r436216 * r436220;
        double r436222 = r436213 - r436221;
        return r436222;
}
↓
double f(double x, double y, double z, double t) {
        double r436223 = x;
        double r436224 = r436223 * r436223;
        double r436225 = y;
        double r436226 = 4.0;
        double r436227 = r436225 * r436226;
        double r436228 = z;
        double r436229 = r436227 * r436228;
        double r436230 = r436229 * r436228;
        double r436231 = r436224 - r436230;
        double r436232 = t;
        double r436233 = -r436232;
        double r436234 = r436233 * r436227;
        double r436235 = r436231 - r436234;
        return r436235;
}

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

Original6.3
Target6.3
Herbie0.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 6.3

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

  3. Applied sub-neg6.3

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

  4. Applied distribute-rgt-in6.3

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

  5. Applied associate--r+6.3

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

  6. Simplified6.3

    \[\leadsto \color{blue}{\left(x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z\right)\right)} - \left(-t\right) \cdot \left(y \cdot 4\right)\]
  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 2019326 
(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))))