Average Error: 0.1 → 0.1
Time: 5.2s
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 r365558 = x;
        double r365559 = y;
        double r365560 = r365558 * r365559;
        double r365561 = z;
        double r365562 = r365561 * r365561;
        double r365563 = r365560 + r365562;
        double r365564 = r365563 + r365562;
        double r365565 = r365564 + r365562;
        return r365565;
}
↓
double f(double x, double y, double z) {
        double r365566 = x;
        double r365567 = y;
        double r365568 = r365566 * r365567;
        double r365569 = z;
        double r365570 = r365569 * r365569;
        double r365571 = r365568 + r365570;
        double r365572 = r365571 + r365570;
        double r365573 = r365572 + r365570;
        return r365573;
}

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 2020046 
(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)))