Average Error: 6.1 → 0.1
Time: 19.5s
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 r418104 = x;
        double r418105 = r418104 * r418104;
        double r418106 = y;
        double r418107 = 4.0;
        double r418108 = r418106 * r418107;
        double r418109 = z;
        double r418110 = r418109 * r418109;
        double r418111 = t;
        double r418112 = r418110 - r418111;
        double r418113 = r418108 * r418112;
        double r418114 = r418105 - r418113;
        return r418114;
}
↓
double f(double x, double y, double z, double t) {
        double r418115 = x;
        double r418116 = r418115 * r418115;
        double r418117 = y;
        double r418118 = 4.0;
        double r418119 = r418117 * r418118;
        double r418120 = z;
        double r418121 = r418119 * r418120;
        double r418122 = r418121 * r418120;
        double r418123 = r418116 - r418122;
        double r418124 = t;
        double r418125 = -r418124;
        double r418126 = r418125 * r418119;
        double r418127 = r418123 - r418126;
        return r418127;
}

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

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

Derivation

  1. Initial program 6.1

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

  3. Applied sub-neg6.1

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

  4. Applied distribute-rgt-in6.1

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

  5. Applied associate--r+6.1

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

  6. Simplified6.1

    \[\leadsto \color{blue}{\left(x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z\right)\right)} - \left(-t\right) \cdot \left(y \cdot 4\right)\]
  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 2019323 
(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))))