Average Error: 13.0 → 0.0
Time: 1.3s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r577238 = x;
        double r577239 = y;
        double r577240 = r577238 * r577239;
        double r577241 = r577239 * r577239;
        double r577242 = r577240 - r577241;
        double r577243 = r577242 + r577241;
        double r577244 = z;
        double r577245 = r577239 * r577244;
        double r577246 = r577243 - r577245;
        return r577246;
}
↓
double f(double x, double y, double z) {
        double r577247 = y;
        double r577248 = x;
        double r577249 = z;
        double r577250 = r577248 - r577249;
        double r577251 = r577247 * r577250;
        return r577251;
}

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

Original13.0
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

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

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