Average Error: 18.0 → 0.0
Time: 23.1s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot \left(-z\right) + x \cdot y\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot \left(-z\right) + x \cdot y
double f(double x, double y, double z) {
        double r17653263 = x;
        double r17653264 = y;
        double r17653265 = r17653263 * r17653264;
        double r17653266 = r17653264 * r17653264;
        double r17653267 = r17653265 + r17653266;
        double r17653268 = z;
        double r17653269 = r17653264 * r17653268;
        double r17653270 = r17653267 - r17653269;
        double r17653271 = r17653270 - r17653266;
        return r17653271;
}
↓
double f(double x, double y, double z) {
        double r17653272 = y;
        double r17653273 = z;
        double r17653274 = -r17653273;
        double r17653275 = r17653272 * r17653274;
        double r17653276 = x;
        double r17653277 = r17653276 * r17653272;
        double r17653278 = r17653275 + r17653277;
        return r17653278;
}

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

Original18.0
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 18.0

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

  2. Simplified0.0

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

  4. Applied sub-neg0.0

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

  5. Applied distribute-rgt-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"

  :herbie-target
  (* (- x z) y)

  (- (- (+ (* x y) (* y y)) (* y z)) (* y y)))