Average Error: 0.1 → 0.1
Time: 3.4s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(x \cdot y + z \cdot z\right) + z \cdot \left(z + z\right)\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(x \cdot y + z \cdot z\right) + z \cdot \left(z + z\right)
double f(double x, double y, double z) {
        double r482096 = x;
        double r482097 = y;
        double r482098 = r482096 * r482097;
        double r482099 = z;
        double r482100 = r482099 * r482099;
        double r482101 = r482098 + r482100;
        double r482102 = r482101 + r482100;
        double r482103 = r482102 + r482100;
        return r482103;
}
↓
double f(double x, double y, double z) {
        double r482104 = x;
        double r482105 = y;
        double r482106 = r482104 * r482105;
        double r482107 = z;
        double r482108 = r482107 * r482107;
        double r482109 = r482106 + r482108;
        double r482110 = r482107 + r482107;
        double r482111 = r482107 * r482110;
        double r482112 = r482109 + r482111;
        return r482112;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(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)))