Average Error: 0.0 → 0.0
Time: 10.9s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2105019 = x;
        double r2105020 = y;
        double r2105021 = r2105019 * r2105020;
        double r2105022 = z;
        double r2105023 = t;
        double r2105024 = r2105022 * r2105023;
        double r2105025 = r2105021 + r2105024;
        double r2105026 = a;
        double r2105027 = b;
        double r2105028 = r2105026 * r2105027;
        double r2105029 = r2105025 + r2105028;
        double r2105030 = c;
        double r2105031 = i;
        double r2105032 = r2105030 * r2105031;
        double r2105033 = r2105029 + r2105032;
        return r2105033;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2105034 = z;
        double r2105035 = t;
        double r2105036 = x;
        double r2105037 = y;
        double r2105038 = c;
        double r2105039 = i;
        double r2105040 = b;
        double r2105041 = a;
        double r2105042 = r2105040 * r2105041;
        double r2105043 = fma(r2105038, r2105039, r2105042);
        double r2105044 = fma(r2105036, r2105037, r2105043);
        double r2105045 = fma(r2105034, r2105035, r2105044);
        return r2105045;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))