Average Error: 5.4 → 0.1
Time: 15.4s
Precision: 64
\[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]
↓
\[x \cdot x - \left(z \cdot \left(\left(y \cdot 4.0\right) \cdot z\right) + \left(y \cdot 4.0\right) \cdot \left(-t\right)\right)\]
x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)
↓
x \cdot x - \left(z \cdot \left(\left(y \cdot 4.0\right) \cdot z\right) + \left(y \cdot 4.0\right) \cdot \left(-t\right)\right)
double f(double x, double y, double z, double t) {
        double r31791594 = x;
        double r31791595 = r31791594 * r31791594;
        double r31791596 = y;
        double r31791597 = 4.0;
        double r31791598 = r31791596 * r31791597;
        double r31791599 = z;
        double r31791600 = r31791599 * r31791599;
        double r31791601 = t;
        double r31791602 = r31791600 - r31791601;
        double r31791603 = r31791598 * r31791602;
        double r31791604 = r31791595 - r31791603;
        return r31791604;
}
↓
double f(double x, double y, double z, double t) {
        double r31791605 = x;
        double r31791606 = r31791605 * r31791605;
        double r31791607 = z;
        double r31791608 = y;
        double r31791609 = 4.0;
        double r31791610 = r31791608 * r31791609;
        double r31791611 = r31791610 * r31791607;
        double r31791612 = r31791607 * r31791611;
        double r31791613 = t;
        double r31791614 = -r31791613;
        double r31791615 = r31791610 * r31791614;
        double r31791616 = r31791612 + r31791615;
        double r31791617 = r31791606 - r31791616;
        return r31791617;
}

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

Original5.4
Target5.4
Herbie0.1
\[x \cdot x - 4.0 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 5.4

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

  3. Applied sub-neg5.4

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

  4. Applied distribute-lft-in5.4

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

  6. Applied associate-*r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 
(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))))