Average Error: 0.0 → 0.0
Time: 14.0s
Precision: 64
\[\left(x \cdot y + z \cdot t\right) + a \cdot b\]
↓
\[\left(a \cdot b + z \cdot t\right) + x \cdot y\]
\left(x \cdot y + z \cdot t\right) + a \cdot b
↓
\left(a \cdot b + z \cdot t\right) + x \cdot y
double f(double x, double y, double z, double t, double a, double b) {
        double r105930 = x;
        double r105931 = y;
        double r105932 = r105930 * r105931;
        double r105933 = z;
        double r105934 = t;
        double r105935 = r105933 * r105934;
        double r105936 = r105932 + r105935;
        double r105937 = a;
        double r105938 = b;
        double r105939 = r105937 * r105938;
        double r105940 = r105936 + r105939;
        return r105940;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r105941 = a;
        double r105942 = b;
        double r105943 = r105941 * r105942;
        double r105944 = z;
        double r105945 = t;
        double r105946 = r105944 * r105945;
        double r105947 = r105943 + r105946;
        double r105948 = x;
        double r105949 = y;
        double r105950 = r105948 * r105949;
        double r105951 = r105947 + r105950;
        return r105951;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(x \cdot y + z \cdot t\right) + a \cdot b\]

  2. Simplified0.0

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

  3. Taylor expanded around inf 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

    \[\leadsto \left(a \cdot b + z \cdot t\right) + x \cdot y\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z t a b)
  :name "Linear.V3:$cdot from linear-1.19.1.3, B"
  (+ (+ (* x y) (* z t)) (* a b)))