Average Error: 13.4 → 0.0
Time: 27.9s
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 r346237 = x;
        double r346238 = y;
        double r346239 = r346237 * r346238;
        double r346240 = r346238 * r346238;
        double r346241 = r346239 - r346240;
        double r346242 = r346241 + r346240;
        double r346243 = z;
        double r346244 = r346238 * r346243;
        double r346245 = r346242 - r346244;
        return r346245;
}
↓
double f(double x, double y, double z) {
        double r346246 = y;
        double r346247 = x;
        double r346248 = r346246 * r346247;
        double r346249 = z;
        double r346250 = r346246 * r346249;
        double r346251 = r346248 - r346250;
        return r346251;
}

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 +o rules:numerics
(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)))