Average Error: 13.1 → 0.0
Time: 15.1s
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 r384178 = x;
        double r384179 = y;
        double r384180 = r384178 * r384179;
        double r384181 = r384179 * r384179;
        double r384182 = r384180 - r384181;
        double r384183 = r384182 + r384181;
        double r384184 = z;
        double r384185 = r384179 * r384184;
        double r384186 = r384183 - r384185;
        return r384186;
}
↓
double f(double x, double y, double z) {
        double r384187 = x;
        double r384188 = z;
        double r384189 = r384187 - r384188;
        double r384190 = y;
        double r384191 = r384189 * r384190;
        return r384191;
}

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

Original13.1
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.1

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

  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 2019305 
(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)))