Average Error: 17.2 → 0.0
Time: 30.7s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r83730241 = x;
        double r83730242 = y;
        double r83730243 = r83730241 * r83730242;
        double r83730244 = r83730242 * r83730242;
        double r83730245 = r83730243 + r83730244;
        double r83730246 = z;
        double r83730247 = r83730242 * r83730246;
        double r83730248 = r83730245 - r83730247;
        double r83730249 = r83730248 - r83730244;
        return r83730249;
}
↓
double f(double x, double y, double z) {
        double r83730250 = y;
        double r83730251 = x;
        double r83730252 = z;
        double r83730253 = r83730251 - r83730252;
        double r83730254 = r83730250 * r83730253;
        return r83730254;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

Enter valid numbers for all inputs

Target

Original17.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.2

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

  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 2019173 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"

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

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