Average Error: 0.0 → 0.0
Time: 3.0s
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 r59572 = x;
        double r59573 = y;
        double r59574 = r59572 * r59573;
        double r59575 = z;
        double r59576 = t;
        double r59577 = r59575 * r59576;
        double r59578 = r59574 + r59577;
        double r59579 = a;
        double r59580 = b;
        double r59581 = r59579 * r59580;
        double r59582 = r59578 + r59581;
        double r59583 = c;
        double r59584 = i;
        double r59585 = r59583 * r59584;
        double r59586 = r59582 + r59585;
        return r59586;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59587 = c;
        double r59588 = i;
        double r59589 = a;
        double r59590 = b;
        double r59591 = x;
        double r59592 = y;
        double r59593 = z;
        double r59594 = t;
        double r59595 = r59593 * r59594;
        double r59596 = fma(r59591, r59592, r59595);
        double r59597 = fma(r59589, r59590, r59596);
        double r59598 = fma(r59587, r59588, r59597);
        return r59598;
}

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 2020046 +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)))