Average Error: 0.0 → 0.0
Time: 15.5s
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 r93190 = x;
        double r93191 = y;
        double r93192 = r93190 * r93191;
        double r93193 = z;
        double r93194 = t;
        double r93195 = r93193 * r93194;
        double r93196 = r93192 + r93195;
        double r93197 = a;
        double r93198 = b;
        double r93199 = r93197 * r93198;
        double r93200 = r93196 + r93199;
        double r93201 = c;
        double r93202 = i;
        double r93203 = r93201 * r93202;
        double r93204 = r93200 + r93203;
        return r93204;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r93205 = c;
        double r93206 = i;
        double r93207 = a;
        double r93208 = b;
        double r93209 = x;
        double r93210 = y;
        double r93211 = z;
        double r93212 = t;
        double r93213 = r93211 * r93212;
        double r93214 = fma(r93209, r93210, r93213);
        double r93215 = fma(r93207, r93208, r93214);
        double r93216 = fma(r93205, r93206, r93215);
        return r93216;
}

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 2019304 +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)))