Average Error: 0.0 → 0.0
Time: 11.6s
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 r3596621 = x;
        double r3596622 = y;
        double r3596623 = r3596621 * r3596622;
        double r3596624 = z;
        double r3596625 = t;
        double r3596626 = r3596624 * r3596625;
        double r3596627 = r3596623 + r3596626;
        double r3596628 = a;
        double r3596629 = b;
        double r3596630 = r3596628 * r3596629;
        double r3596631 = r3596627 + r3596630;
        double r3596632 = c;
        double r3596633 = i;
        double r3596634 = r3596632 * r3596633;
        double r3596635 = r3596631 + r3596634;
        return r3596635;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3596636 = z;
        double r3596637 = t;
        double r3596638 = x;
        double r3596639 = y;
        double r3596640 = c;
        double r3596641 = i;
        double r3596642 = b;
        double r3596643 = a;
        double r3596644 = r3596642 * r3596643;
        double r3596645 = fma(r3596640, r3596641, r3596644);
        double r3596646 = fma(r3596638, r3596639, r3596645);
        double r3596647 = fma(r3596636, r3596637, r3596646);
        return r3596647;
}

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 2019143 +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)))