Average Error: 12.9 → 0.0
Time: 1.7s
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 r488051 = x;
        double r488052 = y;
        double r488053 = r488051 * r488052;
        double r488054 = r488052 * r488052;
        double r488055 = r488053 - r488054;
        double r488056 = r488055 + r488054;
        double r488057 = z;
        double r488058 = r488052 * r488057;
        double r488059 = r488056 - r488058;
        return r488059;
}
↓
double f(double x, double y, double z) {
        double r488060 = y;
        double r488061 = x;
        double r488062 = z;
        double r488063 = r488061 - r488062;
        double r488064 = r488060 * r488063;
        return r488064;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 
(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)))