Average Error: 5.4 → 0.1
Time: 17.4s
Precision: 64
\[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\left(x \cdot x + \left(t \cdot 4.0\right) \cdot y\right) - z \cdot \left(\left(4.0 \cdot y\right) \cdot z\right)\]
x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)
↓
\left(x \cdot x + \left(t \cdot 4.0\right) \cdot y\right) - z \cdot \left(\left(4.0 \cdot y\right) \cdot z\right)
double f(double x, double y, double z, double t) {
        double r35639114 = x;
        double r35639115 = r35639114 * r35639114;
        double r35639116 = y;
        double r35639117 = 4.0;
        double r35639118 = r35639116 * r35639117;
        double r35639119 = z;
        double r35639120 = r35639119 * r35639119;
        double r35639121 = t;
        double r35639122 = r35639120 - r35639121;
        double r35639123 = r35639118 * r35639122;
        double r35639124 = r35639115 - r35639123;
        return r35639124;
}
↓
double f(double x, double y, double z, double t) {
        double r35639125 = x;
        double r35639126 = r35639125 * r35639125;
        double r35639127 = t;
        double r35639128 = 4.0;
        double r35639129 = r35639127 * r35639128;
        double r35639130 = y;
        double r35639131 = r35639129 * r35639130;
        double r35639132 = r35639126 + r35639131;
        double r35639133 = z;
        double r35639134 = r35639128 * r35639130;
        double r35639135 = r35639134 * r35639133;
        double r35639136 = r35639133 * r35639135;
        double r35639137 = r35639132 - r35639136;
        return r35639137;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.4
Target5.4
Herbie0.1
\[x \cdot x - 4.0 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 5.4

    \[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]

  2. Taylor expanded around inf 5.4

    \[\leadsto \color{blue}{\left(4.0 \cdot \left(t \cdot y\right) + {x}^{2}\right) - 4.0 \cdot \left({z}^{2} \cdot y\right)}\]

  3. Simplified0.1

    \[\leadsto \color{blue}{\left(x \cdot x + \left(t \cdot 4.0\right) \cdot y\right) - z \cdot \left(z \cdot \left(4.0 \cdot y\right)\right)}\]

  4. Final simplification0.1

    \[\leadsto \left(x \cdot x + \left(t \cdot 4.0\right) \cdot y\right) - z \cdot \left(\left(4.0 \cdot y\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019164 
(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))))