Average Error: 13.4 → 0.0
Time: 21.7s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot x - y \cdot z\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot x - y \cdot z
double f(double x, double y, double z) {
        double r331186 = x;
        double r331187 = y;
        double r331188 = r331186 * r331187;
        double r331189 = r331187 * r331187;
        double r331190 = r331188 - r331189;
        double r331191 = r331190 + r331189;
        double r331192 = z;
        double r331193 = r331187 * r331192;
        double r331194 = r331191 - r331193;
        return r331194;
}
↓
double f(double x, double y, double z) {
        double r331195 = y;
        double r331196 = x;
        double r331197 = r331195 * r331196;
        double r331198 = z;
        double r331199 = r331195 * r331198;
        double r331200 = r331197 - r331199;
        return r331200;
}

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

Original13.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.4

    \[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
  2. Using strategy rm

  3. Applied associate-+l-8.3

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

  4. Simplified0.0

    \[\leadsto \left(x \cdot y - \color{blue}{0}\right) - y \cdot z\]

  5. Final simplification0.0

    \[\leadsto y \cdot x - y \cdot z\]

Reproduce

herbie shell --seed 2019325 
(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)))