Average Error: 5.9 → 0.1
Time: 3.8s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\left(x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right) - \left(-t\right) \cdot \left(y \cdot 4\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\left(x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right) - \left(-t\right) \cdot \left(y \cdot 4\right)
double f(double x, double y, double z, double t) {
        double r694997 = x;
        double r694998 = r694997 * r694997;
        double r694999 = y;
        double r695000 = 4.0;
        double r695001 = r694999 * r695000;
        double r695002 = z;
        double r695003 = r695002 * r695002;
        double r695004 = t;
        double r695005 = r695003 - r695004;
        double r695006 = r695001 * r695005;
        double r695007 = r694998 - r695006;
        return r695007;
}
↓
double f(double x, double y, double z, double t) {
        double r695008 = x;
        double r695009 = r695008 * r695008;
        double r695010 = z;
        double r695011 = y;
        double r695012 = 4.0;
        double r695013 = r695011 * r695012;
        double r695014 = r695010 * r695013;
        double r695015 = r695010 * r695014;
        double r695016 = r695009 - r695015;
        double r695017 = t;
        double r695018 = -r695017;
        double r695019 = r695018 * r695013;
        double r695020 = r695016 - r695019;
        return r695020;
}

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

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-rgt-in5.9

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

  5. Applied associate--r+5.9

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

  7. Applied associate-*l*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(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))))