Average Error: 12.4 → 0.0
Time: 10.7s
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 r694840 = x;
        double r694841 = y;
        double r694842 = r694840 * r694841;
        double r694843 = r694841 * r694841;
        double r694844 = r694842 - r694843;
        double r694845 = r694844 + r694843;
        double r694846 = z;
        double r694847 = r694841 * r694846;
        double r694848 = r694845 - r694847;
        return r694848;
}
↓
double f(double x, double y, double z) {
        double r694849 = x;
        double r694850 = z;
        double r694851 = r694849 - r694850;
        double r694852 = y;
        double r694853 = r694851 * r694852;
        return r694853;
}

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

Original12.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.4

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

  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 2020047 
(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)))