Average Error: 6.0 → 0.1
Time: 12.8s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[x \cdot x + \left(t \cdot \left(y \cdot 4\right) - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
x \cdot x + \left(t \cdot \left(y \cdot 4\right) - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right)
double f(double x, double y, double z, double t) {
        double r45885492 = x;
        double r45885493 = r45885492 * r45885492;
        double r45885494 = y;
        double r45885495 = 4.0;
        double r45885496 = r45885494 * r45885495;
        double r45885497 = z;
        double r45885498 = r45885497 * r45885497;
        double r45885499 = t;
        double r45885500 = r45885498 - r45885499;
        double r45885501 = r45885496 * r45885500;
        double r45885502 = r45885493 - r45885501;
        return r45885502;
}
↓
double f(double x, double y, double z, double t) {
        double r45885503 = x;
        double r45885504 = r45885503 * r45885503;
        double r45885505 = t;
        double r45885506 = y;
        double r45885507 = 4.0;
        double r45885508 = r45885506 * r45885507;
        double r45885509 = r45885505 * r45885508;
        double r45885510 = z;
        double r45885511 = r45885510 * r45885508;
        double r45885512 = r45885510 * r45885511;
        double r45885513 = r45885509 - r45885512;
        double r45885514 = r45885504 + r45885513;
        return r45885514;
}

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

Original6.0
Target6.0
Herbie0.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 6.0

    \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]

  2. Taylor expanded around inf 6.0

    \[\leadsto \color{blue}{\left(4 \cdot \left(t \cdot y\right) + {x}^{2}\right) - 4 \cdot \left({z}^{2} \cdot y\right)}\]

  3. Simplified6.0

    \[\leadsto \color{blue}{x \cdot x + \left(t \cdot \left(y \cdot 4\right) - \left(z \cdot z\right) \cdot \left(y \cdot 4\right)\right)}\]
  4. Using strategy rm

  5. Applied associate-*l*0.1

    \[\leadsto x \cdot x + \left(t \cdot \left(y \cdot 4\right) - \color{blue}{z \cdot \left(z \cdot \left(y \cdot 4\right)\right)}\right)\]

  6. Final simplification0.1

    \[\leadsto x \cdot x + \left(t \cdot \left(y \cdot 4\right) - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right)\]

Reproduce

herbie shell --seed 2019174 
(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))))