Average Error: 5.3 → 0.1
Time: 9.2s
Precision: 64
\[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]
↓
\[x \cdot x - \left(\left(z \cdot \left(y \cdot 4.0\right)\right) \cdot z + \left(-t \cdot \left(y \cdot 4.0\right)\right)\right)\]
x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)
↓
x \cdot x - \left(\left(z \cdot \left(y \cdot 4.0\right)\right) \cdot z + \left(-t \cdot \left(y \cdot 4.0\right)\right)\right)
double f(double x, double y, double z, double t) {
        double r12856263 = x;
        double r12856264 = r12856263 * r12856263;
        double r12856265 = y;
        double r12856266 = 4.0;
        double r12856267 = r12856265 * r12856266;
        double r12856268 = z;
        double r12856269 = r12856268 * r12856268;
        double r12856270 = t;
        double r12856271 = r12856269 - r12856270;
        double r12856272 = r12856267 * r12856271;
        double r12856273 = r12856264 - r12856272;
        return r12856273;
}
↓
double f(double x, double y, double z, double t) {
        double r12856274 = x;
        double r12856275 = r12856274 * r12856274;
        double r12856276 = z;
        double r12856277 = y;
        double r12856278 = 4.0;
        double r12856279 = r12856277 * r12856278;
        double r12856280 = r12856276 * r12856279;
        double r12856281 = r12856280 * r12856276;
        double r12856282 = t;
        double r12856283 = r12856282 * r12856279;
        double r12856284 = -r12856283;
        double r12856285 = r12856281 + r12856284;
        double r12856286 = r12856275 - r12856285;
        return r12856286;
}

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

Original5.3
Target5.2
Herbie0.1
\[x \cdot x - 4.0 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 5.3

    \[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]
  2. Using strategy rm

  3. Applied sub-neg5.3

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

  4. Applied distribute-lft-in5.3

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

  5. Taylor expanded around 0 5.3

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019156 
(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))))