Average Error: 0.0 → 0.0
Time: 18.8s
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 r66195 = x;
        double r66196 = y;
        double r66197 = r66195 * r66196;
        double r66198 = z;
        double r66199 = t;
        double r66200 = r66198 * r66199;
        double r66201 = r66197 + r66200;
        double r66202 = a;
        double r66203 = b;
        double r66204 = r66202 * r66203;
        double r66205 = r66201 + r66204;
        double r66206 = c;
        double r66207 = i;
        double r66208 = r66206 * r66207;
        double r66209 = r66205 + r66208;
        return r66209;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r66210 = c;
        double r66211 = i;
        double r66212 = a;
        double r66213 = b;
        double r66214 = x;
        double r66215 = y;
        double r66216 = z;
        double r66217 = t;
        double r66218 = r66216 * r66217;
        double r66219 = fma(r66214, r66215, r66218);
        double r66220 = fma(r66212, r66213, r66219);
        double r66221 = fma(r66210, r66211, r66220);
        return r66221;
}

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 2019305 +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)))