Average Error: 0.1 → 0.1
Time: 3.2s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(3 \cdot z\right) \cdot z + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(3 \cdot z\right) \cdot z + x \cdot y
double f(double x, double y, double z) {
        double r481128 = x;
        double r481129 = y;
        double r481130 = r481128 * r481129;
        double r481131 = z;
        double r481132 = r481131 * r481131;
        double r481133 = r481130 + r481132;
        double r481134 = r481133 + r481132;
        double r481135 = r481134 + r481132;
        return r481135;
}
↓
double f(double x, double y, double z) {
        double r481136 = 3.0;
        double r481137 = z;
        double r481138 = r481136 * r481137;
        double r481139 = r481138 * r481137;
        double r481140 = x;
        double r481141 = y;
        double r481142 = r481140 * r481141;
        double r481143 = r481139 + r481142;
        return r481143;
}

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. Simplified0.1

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

  4. Applied associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 
(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)))