Average Error: 0.0 → 0.0
Time: 11.5s
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 r103217 = x;
        double r103218 = y;
        double r103219 = r103217 * r103218;
        double r103220 = z;
        double r103221 = t;
        double r103222 = r103220 * r103221;
        double r103223 = r103219 + r103222;
        double r103224 = a;
        double r103225 = b;
        double r103226 = r103224 * r103225;
        double r103227 = r103223 + r103226;
        double r103228 = c;
        double r103229 = i;
        double r103230 = r103228 * r103229;
        double r103231 = r103227 + r103230;
        return r103231;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r103232 = c;
        double r103233 = i;
        double r103234 = a;
        double r103235 = b;
        double r103236 = x;
        double r103237 = y;
        double r103238 = z;
        double r103239 = t;
        double r103240 = r103238 * r103239;
        double r103241 = fma(r103236, r103237, r103240);
        double r103242 = fma(r103234, r103235, r103241);
        double r103243 = fma(r103232, r103233, r103242);
        return r103243;
}

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 2020045 +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)))