Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(i, c, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, t \cdot z\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(i, c, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, t \cdot z\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r104645 = x;
        double r104646 = y;
        double r104647 = r104645 * r104646;
        double r104648 = z;
        double r104649 = t;
        double r104650 = r104648 * r104649;
        double r104651 = r104647 + r104650;
        double r104652 = a;
        double r104653 = b;
        double r104654 = r104652 * r104653;
        double r104655 = r104651 + r104654;
        double r104656 = c;
        double r104657 = i;
        double r104658 = r104656 * r104657;
        double r104659 = r104655 + r104658;
        return r104659;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r104660 = i;
        double r104661 = c;
        double r104662 = a;
        double r104663 = b;
        double r104664 = x;
        double r104665 = y;
        double r104666 = t;
        double r104667 = z;
        double r104668 = r104666 * r104667;
        double r104669 = fma(r104664, r104665, r104668);
        double r104670 = fma(r104662, r104663, r104669);
        double r104671 = fma(r104660, r104661, r104670);
        return r104671;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +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)))