Average Error: 5.5 → 0.2
Time: 16.1s
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 r30837188 = x;
        double r30837189 = r30837188 * r30837188;
        double r30837190 = y;
        double r30837191 = 4.0;
        double r30837192 = r30837190 * r30837191;
        double r30837193 = z;
        double r30837194 = r30837193 * r30837193;
        double r30837195 = t;
        double r30837196 = r30837194 - r30837195;
        double r30837197 = r30837192 * r30837196;
        double r30837198 = r30837189 - r30837197;
        return r30837198;
}
↓
double f(double x, double y, double z, double t) {
        double r30837199 = x;
        double r30837200 = r30837199 * r30837199;
        double r30837201 = t;
        double r30837202 = 4.0;
        double r30837203 = r30837201 * r30837202;
        double r30837204 = y;
        double r30837205 = r30837203 * r30837204;
        double r30837206 = r30837200 + r30837205;
        double r30837207 = z;
        double r30837208 = r30837202 * r30837204;
        double r30837209 = r30837208 * r30837207;
        double r30837210 = r30837207 * r30837209;
        double r30837211 = r30837206 - r30837210;
        return r30837211;
}

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

Original5.5
Target5.5
Herbie0.2
\[x \cdot x - 4.0 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 5.5

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

  2. Taylor expanded around inf 5.5

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019162 
(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))))