Average Error: 13.2 → 0.0
Time: 20.9s
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 r361301 = x;
        double r361302 = y;
        double r361303 = r361301 * r361302;
        double r361304 = r361302 * r361302;
        double r361305 = r361303 - r361304;
        double r361306 = r361305 + r361304;
        double r361307 = z;
        double r361308 = r361302 * r361307;
        double r361309 = r361306 - r361308;
        return r361309;
}
↓
double f(double x, double y, double z) {
        double r361310 = y;
        double r361311 = x;
        double r361312 = z;
        double r361313 = r361311 - r361312;
        double r361314 = r361310 * r361313;
        return r361314;
}

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

Original13.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.2

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

  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 2019235 +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)))