Average Error: 17.0 → 0.0
Time: 16.6s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r338293 = x;
        double r338294 = y;
        double r338295 = r338293 * r338294;
        double r338296 = z;
        double r338297 = r338294 * r338296;
        double r338298 = r338295 - r338297;
        double r338299 = r338294 * r338294;
        double r338300 = r338298 - r338299;
        double r338301 = r338300 + r338299;
        return r338301;
}
↓
double f(double x, double y, double z) {
        double r338302 = x;
        double r338303 = z;
        double r338304 = r338302 - r338303;
        double r338305 = y;
        double r338306 = r338304 * r338305;
        return r338306;
}

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

Original17.0
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (+ (- (- (* x y) (* y z)) (* y y)) (* y y)))