Average Error: 12.8 → 0.0
Time: 1.8s
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 r527057 = x;
        double r527058 = y;
        double r527059 = r527057 * r527058;
        double r527060 = r527058 * r527058;
        double r527061 = r527059 - r527060;
        double r527062 = r527061 + r527060;
        double r527063 = z;
        double r527064 = r527058 * r527063;
        double r527065 = r527062 - r527064;
        return r527065;
}
↓
double f(double x, double y, double z) {
        double r527066 = y;
        double r527067 = x;
        double r527068 = z;
        double r527069 = r527067 - r527068;
        double r527070 = r527066 * r527069;
        return r527070;
}

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

Original12.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.8

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

  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 2020083 
(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)))