Average Error: 0.0 → 0.0
Time: 13.0s
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 r48018 = x;
        double r48019 = y;
        double r48020 = r48018 * r48019;
        double r48021 = z;
        double r48022 = t;
        double r48023 = r48021 * r48022;
        double r48024 = r48020 + r48023;
        double r48025 = a;
        double r48026 = b;
        double r48027 = r48025 * r48026;
        double r48028 = r48024 + r48027;
        double r48029 = c;
        double r48030 = i;
        double r48031 = r48029 * r48030;
        double r48032 = r48028 + r48031;
        return r48032;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r48033 = c;
        double r48034 = i;
        double r48035 = a;
        double r48036 = b;
        double r48037 = x;
        double r48038 = y;
        double r48039 = z;
        double r48040 = t;
        double r48041 = r48039 * r48040;
        double r48042 = fma(r48037, r48038, r48041);
        double r48043 = fma(r48035, r48036, r48042);
        double r48044 = fma(r48033, r48034, r48043);
        return r48044;
}

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 2019306 +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)))