Average Error: 0.1 → 0.1
Time: 3.0s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[x \cdot y + \left(3 \cdot z\right) \cdot z\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
x \cdot y + \left(3 \cdot z\right) \cdot z
double f(double x, double y, double z) {
        double r1054602 = x;
        double r1054603 = y;
        double r1054604 = r1054602 * r1054603;
        double r1054605 = z;
        double r1054606 = r1054605 * r1054605;
        double r1054607 = r1054604 + r1054606;
        double r1054608 = r1054607 + r1054606;
        double r1054609 = r1054608 + r1054606;
        return r1054609;
}
↓
double f(double x, double y, double z) {
        double r1054610 = x;
        double r1054611 = y;
        double r1054612 = r1054610 * r1054611;
        double r1054613 = 3.0;
        double r1054614 = z;
        double r1054615 = r1054613 * r1054614;
        double r1054616 = r1054615 * r1054614;
        double r1054617 = r1054612 + r1054616;
        return r1054617;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\left(3 \cdot z\right) \cdot z + y \cdot x\]

Derivation

  1. Initial program 0.1

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

  3. Applied associate-+l+0.1

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

  4. Simplified0.1

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

  6. Applied associate-+l+0.1

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

  7. Simplified0.1

    \[\leadsto x \cdot y + \color{blue}{\left(3 \cdot z\right) \cdot z}\]

  8. Final simplification0.1

    \[\leadsto x \cdot y + \left(3 \cdot z\right) \cdot z\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (+ (* (* 3 z) z) (* y x))

  (+ (+ (+ (* x y) (* z z)) (* z z)) (* z z)))