Average Error: 0.0 → 0.0
Time: 5.0s
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 r86230 = x;
        double r86231 = y;
        double r86232 = r86230 * r86231;
        double r86233 = z;
        double r86234 = t;
        double r86235 = r86233 * r86234;
        double r86236 = r86232 + r86235;
        double r86237 = a;
        double r86238 = b;
        double r86239 = r86237 * r86238;
        double r86240 = r86236 + r86239;
        double r86241 = c;
        double r86242 = i;
        double r86243 = r86241 * r86242;
        double r86244 = r86240 + r86243;
        return r86244;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r86245 = c;
        double r86246 = i;
        double r86247 = a;
        double r86248 = b;
        double r86249 = x;
        double r86250 = y;
        double r86251 = z;
        double r86252 = t;
        double r86253 = r86251 * r86252;
        double r86254 = fma(r86249, r86250, r86253);
        double r86255 = fma(r86247, r86248, r86254);
        double r86256 = fma(r86245, r86246, r86255);
        return r86256;
}

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 2019350 +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)))