Average Error: 5.5 → 0.2
Time: 17.5s
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 r34388609 = x;
        double r34388610 = r34388609 * r34388609;
        double r34388611 = y;
        double r34388612 = 4.0;
        double r34388613 = r34388611 * r34388612;
        double r34388614 = z;
        double r34388615 = r34388614 * r34388614;
        double r34388616 = t;
        double r34388617 = r34388615 - r34388616;
        double r34388618 = r34388613 * r34388617;
        double r34388619 = r34388610 - r34388618;
        return r34388619;
}
↓
double f(double x, double y, double z, double t) {
        double r34388620 = x;
        double r34388621 = r34388620 * r34388620;
        double r34388622 = t;
        double r34388623 = 4.0;
        double r34388624 = r34388622 * r34388623;
        double r34388625 = y;
        double r34388626 = r34388624 * r34388625;
        double r34388627 = r34388621 + r34388626;
        double r34388628 = z;
        double r34388629 = r34388623 * r34388625;
        double r34388630 = r34388629 * r34388628;
        double r34388631 = r34388628 * r34388630;
        double r34388632 = r34388627 - r34388631;
        return r34388632;
}

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))))