Average Error: 0.0 → 0.0
Time: 4.8s
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 r96015 = x;
        double r96016 = y;
        double r96017 = r96015 * r96016;
        double r96018 = z;
        double r96019 = t;
        double r96020 = r96018 * r96019;
        double r96021 = r96017 + r96020;
        double r96022 = a;
        double r96023 = b;
        double r96024 = r96022 * r96023;
        double r96025 = r96021 + r96024;
        double r96026 = c;
        double r96027 = i;
        double r96028 = r96026 * r96027;
        double r96029 = r96025 + r96028;
        return r96029;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r96030 = c;
        double r96031 = i;
        double r96032 = a;
        double r96033 = b;
        double r96034 = x;
        double r96035 = y;
        double r96036 = z;
        double r96037 = t;
        double r96038 = r96036 * r96037;
        double r96039 = fma(r96034, r96035, r96038);
        double r96040 = fma(r96032, r96033, r96039);
        double r96041 = fma(r96030, r96031, r96040);
        return r96041;
}

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 2020047 +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)))