Average Error: 0.0 → 0.0
Time: 9.3s
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 r58707 = x;
        double r58708 = y;
        double r58709 = r58707 * r58708;
        double r58710 = z;
        double r58711 = t;
        double r58712 = r58710 * r58711;
        double r58713 = r58709 + r58712;
        double r58714 = a;
        double r58715 = b;
        double r58716 = r58714 * r58715;
        double r58717 = r58713 + r58716;
        double r58718 = c;
        double r58719 = i;
        double r58720 = r58718 * r58719;
        double r58721 = r58717 + r58720;
        return r58721;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r58722 = c;
        double r58723 = i;
        double r58724 = a;
        double r58725 = b;
        double r58726 = x;
        double r58727 = y;
        double r58728 = z;
        double r58729 = t;
        double r58730 = r58728 * r58729;
        double r58731 = fma(r58726, r58727, r58730);
        double r58732 = fma(r58724, r58725, r58731);
        double r58733 = fma(r58722, r58723, r58732);
        return r58733;
}

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 2019208 +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)))