Average Error: 0.1 → 0.1
Time: 10.4s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[x \cdot y + 3 \cdot \left(z \cdot z\right)\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
x \cdot y + 3 \cdot \left(z \cdot z\right)
double f(double x, double y, double z) {
        double r968041 = x;
        double r968042 = y;
        double r968043 = r968041 * r968042;
        double r968044 = z;
        double r968045 = r968044 * r968044;
        double r968046 = r968043 + r968045;
        double r968047 = r968046 + r968045;
        double r968048 = r968047 + r968045;
        return r968048;
}
↓
double f(double x, double y, double z) {
        double r968049 = x;
        double r968050 = y;
        double r968051 = r968049 * r968050;
        double r968052 = 3.0;
        double r968053 = z;
        double r968054 = r968053 * r968053;
        double r968055 = r968052 * r968054;
        double r968056 = r968051 + r968055;
        return r968056;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019209 
(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)))