Average Error: 0.0 → 0.0
Time: 15.6s
Precision: 64
\[x \cdot y - z \cdot t\]
↓
\[x \cdot y - t \cdot z\]
x \cdot y - z \cdot t
↓
x \cdot y - t \cdot z
double f(double x, double y, double z, double t) {
        double r13899108 = x;
        double r13899109 = y;
        double r13899110 = r13899108 * r13899109;
        double r13899111 = z;
        double r13899112 = t;
        double r13899113 = r13899111 * r13899112;
        double r13899114 = r13899110 - r13899113;
        return r13899114;
}
↓
double f(double x, double y, double z, double t) {
        double r13899115 = x;
        double r13899116 = y;
        double r13899117 = r13899115 * r13899116;
        double r13899118 = t;
        double r13899119 = z;
        double r13899120 = r13899118 * r13899119;
        double r13899121 = r13899117 - r13899120;
        return r13899121;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot y - z \cdot t\]
  2. Using strategy rm

  3. Applied flip--26.2

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

  4. Taylor expanded around inf 0.0

    \[\leadsto \color{blue}{x \cdot y - t \cdot z}\]

  5. Final simplification0.0

    \[\leadsto x \cdot y - t \cdot z\]

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))