Average Error: 0.0 → 0.0
Time: 5.9s
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 r95080 = x;
        double r95081 = y;
        double r95082 = r95080 * r95081;
        double r95083 = z;
        double r95084 = t;
        double r95085 = r95083 * r95084;
        double r95086 = r95082 + r95085;
        double r95087 = a;
        double r95088 = b;
        double r95089 = r95087 * r95088;
        double r95090 = r95086 + r95089;
        double r95091 = c;
        double r95092 = i;
        double r95093 = r95091 * r95092;
        double r95094 = r95090 + r95093;
        return r95094;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r95095 = c;
        double r95096 = i;
        double r95097 = a;
        double r95098 = b;
        double r95099 = x;
        double r95100 = y;
        double r95101 = z;
        double r95102 = t;
        double r95103 = r95101 * r95102;
        double r95104 = fma(r95099, r95100, r95103);
        double r95105 = fma(r95097, r95098, r95104);
        double r95106 = fma(r95095, r95096, r95105);
        return r95106;
}

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 2020047 +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)))