Average Error: 13.4 → 0.0
Time: 9.9s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r689358 = x;
        double r689359 = y;
        double r689360 = r689358 * r689359;
        double r689361 = r689359 * r689359;
        double r689362 = r689360 - r689361;
        double r689363 = r689362 + r689361;
        double r689364 = z;
        double r689365 = r689359 * r689364;
        double r689366 = r689363 - r689365;
        return r689366;
}
↓
double f(double x, double y, double z) {
        double r689367 = x;
        double r689368 = z;
        double r689369 = r689367 - r689368;
        double r689370 = y;
        double r689371 = r689369 * r689370;
        return r689371;
}

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. 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 2020046 
(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)))