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 r468128 = x;
        double r468129 = y;
        double r468130 = r468128 * r468129;
        double r468131 = r468129 * r468129;
        double r468132 = r468130 - r468131;
        double r468133 = r468132 + r468131;
        double r468134 = z;
        double r468135 = r468129 * r468134;
        double r468136 = r468133 - r468135;
        return r468136;
}
↓
double f(double x, double y, double z) {
        double r468137 = y;
        double r468138 = x;
        double r468139 = z;
        double r468140 = r468138 - r468139;
        double r468141 = r468137 * r468140;
        return r468141;
}

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)))