Average Error: 12.4 → 0.0
Time: 14.0s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r575848 = x;
        double r575849 = y;
        double r575850 = r575848 * r575849;
        double r575851 = r575849 * r575849;
        double r575852 = r575850 - r575851;
        double r575853 = r575852 + r575851;
        double r575854 = z;
        double r575855 = r575849 * r575854;
        double r575856 = r575853 - r575855;
        return r575856;
}
↓
double f(double x, double y, double z) {
        double r575857 = y;
        double r575858 = x;
        double r575859 = z;
        double r575860 = r575858 - r575859;
        double r575861 = r575857 * r575860;
        return r575861;
}

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

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

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(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)))