Average Error: 17.5 → 0.0
Time: 2.0s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r601228 = x;
        double r601229 = y;
        double r601230 = r601228 * r601229;
        double r601231 = z;
        double r601232 = r601229 * r601231;
        double r601233 = r601230 - r601232;
        double r601234 = r601229 * r601229;
        double r601235 = r601233 - r601234;
        double r601236 = r601235 + r601234;
        return r601236;
}
↓
double f(double x, double y, double z) {
        double r601237 = y;
        double r601238 = x;
        double r601239 = z;
        double r601240 = r601238 - r601239;
        double r601241 = r601237 * r601240;
        return r601241;
}

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

Original17.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.5

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

  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 2020083 +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)))