Average Error: 13.1 → 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 r442908 = x;
        double r442909 = y;
        double r442910 = r442908 * r442909;
        double r442911 = r442909 * r442909;
        double r442912 = r442910 - r442911;
        double r442913 = r442912 + r442911;
        double r442914 = z;
        double r442915 = r442909 * r442914;
        double r442916 = r442913 - r442915;
        return r442916;
}
↓
double f(double x, double y, double z) {
        double r442917 = y;
        double r442918 = x;
        double r442919 = z;
        double r442920 = r442918 - r442919;
        double r442921 = r442917 * r442920;
        return r442921;
}

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

Original13.1
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.1

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

  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 2020062 
(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)))