Average Error: 0.1 → 0.1
Time: 4.2s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[3 \cdot \left(z \cdot z\right) + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
3 \cdot \left(z \cdot z\right) + x \cdot y
double f(double x, double y, double z) {
        double r2434 = x;
        double r2435 = y;
        double r2436 = r2434 * r2435;
        double r2437 = z;
        double r2438 = r2437 * r2437;
        double r2439 = r2436 + r2438;
        double r2440 = r2439 + r2438;
        double r2441 = r2440 + r2438;
        return r2441;
}
↓
double f(double x, double y, double z) {
        double r2442 = 3.0;
        double r2443 = z;
        double r2444 = r2443 * r2443;
        double r2445 = r2442 * r2444;
        double r2446 = x;
        double r2447 = y;
        double r2448 = r2446 * r2447;
        double r2449 = r2445 + r2448;
        return r2449;
}

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

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

  4. Applied pow10.1

    \[\leadsto \color{blue}{{\left(3 \cdot \left(z \cdot z\right) + x \cdot y\right)}^{1}}\]

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 
(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)))