Average Error: 12.9 → 0.0
Time: 17.9s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r431051 = x;
        double r431052 = y;
        double r431053 = r431051 * r431052;
        double r431054 = r431052 * r431052;
        double r431055 = r431053 - r431054;
        double r431056 = r431055 + r431054;
        double r431057 = z;
        double r431058 = r431052 * r431057;
        double r431059 = r431056 - r431058;
        return r431059;
}
↓
double f(double x, double y, double z) {
        double r431060 = x;
        double r431061 = z;
        double r431062 = r431060 - r431061;
        double r431063 = y;
        double r431064 = r431062 * r431063;
        return r431064;
}

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

Original12.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.9

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(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)))