Average Error: 0.0 → 0.0
Time: 10.1s
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 r5174156 = x;
        double r5174157 = y;
        double r5174158 = r5174156 * r5174157;
        double r5174159 = z;
        double r5174160 = t;
        double r5174161 = r5174159 * r5174160;
        double r5174162 = r5174158 + r5174161;
        double r5174163 = a;
        double r5174164 = b;
        double r5174165 = r5174163 * r5174164;
        double r5174166 = r5174162 + r5174165;
        double r5174167 = c;
        double r5174168 = i;
        double r5174169 = r5174167 * r5174168;
        double r5174170 = r5174166 + r5174169;
        return r5174170;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r5174171 = z;
        double r5174172 = t;
        double r5174173 = x;
        double r5174174 = y;
        double r5174175 = c;
        double r5174176 = i;
        double r5174177 = b;
        double r5174178 = a;
        double r5174179 = r5174177 * r5174178;
        double r5174180 = fma(r5174175, r5174176, r5174179);
        double r5174181 = fma(r5174173, r5174174, r5174180);
        double r5174182 = fma(r5174171, r5174172, r5174181);
        return r5174182;
}

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 2019158 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))