Average Error: 0.1 → 0.1
Time: 16.2s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[z \cdot \left(z + \left(z + z\right)\right) + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
z \cdot \left(z + \left(z + z\right)\right) + x \cdot y
double f(double x, double y, double z) {
        double r403247 = x;
        double r403248 = y;
        double r403249 = r403247 * r403248;
        double r403250 = z;
        double r403251 = r403250 * r403250;
        double r403252 = r403249 + r403251;
        double r403253 = r403252 + r403251;
        double r403254 = r403253 + r403251;
        return r403254;
}
↓
double f(double x, double y, double z) {
        double r403255 = z;
        double r403256 = r403255 + r403255;
        double r403257 = r403255 + r403256;
        double r403258 = r403255 * r403257;
        double r403259 = x;
        double r403260 = y;
        double r403261 = r403259 * r403260;
        double r403262 = r403258 + r403261;
        return r403262;
}

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

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

Reproduce

herbie shell --seed 2019303 
(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)))