Average Error: 0.0 → 0.0
Time: 12.3s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2328109 = x;
        double r2328110 = y;
        double r2328111 = r2328109 * r2328110;
        double r2328112 = z;
        double r2328113 = t;
        double r2328114 = r2328112 * r2328113;
        double r2328115 = r2328111 + r2328114;
        double r2328116 = a;
        double r2328117 = b;
        double r2328118 = r2328116 * r2328117;
        double r2328119 = r2328115 + r2328118;
        double r2328120 = c;
        double r2328121 = i;
        double r2328122 = r2328120 * r2328121;
        double r2328123 = r2328119 + r2328122;
        return r2328123;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2328124 = z;
        double r2328125 = t;
        double r2328126 = x;
        double r2328127 = y;
        double r2328128 = c;
        double r2328129 = i;
        double r2328130 = b;
        double r2328131 = a;
        double r2328132 = r2328130 * r2328131;
        double r2328133 = fma(r2328128, r2328129, r2328132);
        double r2328134 = fma(r2328126, r2328127, r2328133);
        double r2328135 = fma(r2328124, r2328125, r2328134);
        return r2328135;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, a \cdot b\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))