Average Error: 0.1 → 0.1
Time: 4.5s
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 r473114 = x;
        double r473115 = y;
        double r473116 = r473114 * r473115;
        double r473117 = z;
        double r473118 = r473117 * r473117;
        double r473119 = r473116 + r473118;
        double r473120 = r473119 + r473118;
        double r473121 = r473120 + r473118;
        return r473121;
}
↓
double f(double x, double y, double z) {
        double r473122 = x;
        double r473123 = y;
        double r473124 = r473122 * r473123;
        double r473125 = z;
        double r473126 = r473125 * r473125;
        double r473127 = r473124 + r473126;
        double r473128 = r473127 + r473126;
        double r473129 = r473128 + r473126;
        return r473129;
}

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 2020033 +o rules:numerics
(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)))