Average Error: 6.1 → 0.1
Time: 3.6s
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 r744106 = x;
        double r744107 = r744106 * r744106;
        double r744108 = y;
        double r744109 = 4.0;
        double r744110 = r744108 * r744109;
        double r744111 = z;
        double r744112 = r744111 * r744111;
        double r744113 = t;
        double r744114 = r744112 - r744113;
        double r744115 = r744110 * r744114;
        double r744116 = r744107 - r744115;
        return r744116;
}
↓
double f(double x, double y, double z, double t) {
        double r744117 = x;
        double r744118 = r744117 * r744117;
        double r744119 = z;
        double r744120 = y;
        double r744121 = 4.0;
        double r744122 = r744120 * r744121;
        double r744123 = r744119 * r744122;
        double r744124 = r744119 * r744123;
        double r744125 = r744118 - r744124;
        double r744126 = t;
        double r744127 = -r744126;
        double r744128 = r744127 * r744122;
        double r744129 = r744125 - r744128;
        return r744129;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

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Results

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Target

Original6.1
Target6.0
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. 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 2020060 
(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))))