Average Error: 0.0 → 0.0
Time: 7.3s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r51836 = x;
        double r51837 = y;
        double r51838 = r51836 * r51837;
        double r51839 = z;
        double r51840 = t;
        double r51841 = r51839 * r51840;
        double r51842 = r51838 + r51841;
        double r51843 = a;
        double r51844 = b;
        double r51845 = r51843 * r51844;
        double r51846 = r51842 + r51845;
        double r51847 = c;
        double r51848 = i;
        double r51849 = r51847 * r51848;
        double r51850 = r51846 + r51849;
        return r51850;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r51851 = c;
        double r51852 = i;
        double r51853 = a;
        double r51854 = b;
        double r51855 = x;
        double r51856 = y;
        double r51857 = z;
        double r51858 = t;
        double r51859 = r51857 * r51858;
        double r51860 = fma(r51855, r51856, r51859);
        double r51861 = fma(r51853, r51854, r51860);
        double r51862 = fma(r51851, r51852, r51861);
        return r51862;
}

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

Bits error versus c

Bits error versus i

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))