Average Error: 0.1 → 0.1
Time: 48.6s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
double f(double x, double y, double z) {
        double r459074 = x;
        double r459075 = y;
        double r459076 = r459074 * r459075;
        double r459077 = z;
        double r459078 = r459077 * r459077;
        double r459079 = r459076 + r459078;
        double r459080 = r459079 + r459078;
        double r459081 = r459080 + r459078;
        return r459081;
}
↓
double f(double x, double y, double z) {
        double r459082 = x;
        double r459083 = y;
        double r459084 = r459082 * r459083;
        double r459085 = z;
        double r459086 = r459085 * r459085;
        double r459087 = r459084 + r459086;
        double r459088 = r459087 + r459086;
        double r459089 = r459088 + r459086;
        return r459089;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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)))