Average Error: 0.0 → 0.0
Time: 5.5s
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 r167795 = x;
        double r167796 = y;
        double r167797 = r167795 * r167796;
        double r167798 = z;
        double r167799 = t;
        double r167800 = r167798 * r167799;
        double r167801 = r167797 + r167800;
        double r167802 = a;
        double r167803 = b;
        double r167804 = r167802 * r167803;
        double r167805 = r167801 + r167804;
        double r167806 = c;
        double r167807 = i;
        double r167808 = r167806 * r167807;
        double r167809 = r167805 + r167808;
        return r167809;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r167810 = c;
        double r167811 = i;
        double r167812 = a;
        double r167813 = b;
        double r167814 = x;
        double r167815 = y;
        double r167816 = z;
        double r167817 = t;
        double r167818 = r167816 * r167817;
        double r167819 = fma(r167814, r167815, r167818);
        double r167820 = fma(r167812, r167813, r167819);
        double r167821 = fma(r167810, r167811, r167820);
        return r167821;
}

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 2019350 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))