Average Error: 0.0 → 0.0
Time: 7.1s
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 r54060 = x;
        double r54061 = y;
        double r54062 = r54060 * r54061;
        double r54063 = z;
        double r54064 = t;
        double r54065 = r54063 * r54064;
        double r54066 = r54062 + r54065;
        double r54067 = a;
        double r54068 = b;
        double r54069 = r54067 * r54068;
        double r54070 = r54066 + r54069;
        double r54071 = c;
        double r54072 = i;
        double r54073 = r54071 * r54072;
        double r54074 = r54070 + r54073;
        return r54074;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r54075 = c;
        double r54076 = i;
        double r54077 = a;
        double r54078 = b;
        double r54079 = x;
        double r54080 = y;
        double r54081 = z;
        double r54082 = t;
        double r54083 = r54081 * r54082;
        double r54084 = fma(r54079, r54080, r54083);
        double r54085 = fma(r54077, r54078, r54084);
        double r54086 = fma(r54075, r54076, r54085);
        return r54086;
}

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 2019235 +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)))