Average Error: 6.0 → 0.1
Time: 11.3s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\left(x \cdot x - \left(z \cdot \left(z \cdot y\right)\right) \cdot 4\right) - \left(\left(-4\right) \cdot y\right) \cdot t\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\left(x \cdot x - \left(z \cdot \left(z \cdot y\right)\right) \cdot 4\right) - \left(\left(-4\right) \cdot y\right) \cdot t
double f(double x, double y, double z, double t) {
        double r527464 = x;
        double r527465 = r527464 * r527464;
        double r527466 = y;
        double r527467 = 4.0;
        double r527468 = r527466 * r527467;
        double r527469 = z;
        double r527470 = r527469 * r527469;
        double r527471 = t;
        double r527472 = r527470 - r527471;
        double r527473 = r527468 * r527472;
        double r527474 = r527465 - r527473;
        return r527474;
}
↓
double f(double x, double y, double z, double t) {
        double r527475 = x;
        double r527476 = r527475 * r527475;
        double r527477 = z;
        double r527478 = y;
        double r527479 = r527477 * r527478;
        double r527480 = r527477 * r527479;
        double r527481 = 4.0;
        double r527482 = r527480 * r527481;
        double r527483 = r527476 - r527482;
        double r527484 = -r527481;
        double r527485 = r527484 * r527478;
        double r527486 = t;
        double r527487 = r527485 * r527486;
        double r527488 = r527483 - r527487;
        return r527488;
}

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. Using strategy rm

  3. Applied sub-neg6.0

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

  4. Applied distribute-rgt-in6.0

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

  5. Applied associate--r+6.0

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

  6. Simplified6.0

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

  8. Applied associate-*r*0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

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))))