Average Error: 0.0 → 0.0
Time: 5.0s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(i, c, \left(\mathsf{fma}\left(a, b, \left(\mathsf{fma}\left(x, y, \left(t \cdot z\right)\right)\right)\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(i, c, \left(\mathsf{fma}\left(a, b, \left(\mathsf{fma}\left(x, y, \left(t \cdot z\right)\right)\right)\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r6367557 = x;
        double r6367558 = y;
        double r6367559 = r6367557 * r6367558;
        double r6367560 = z;
        double r6367561 = t;
        double r6367562 = r6367560 * r6367561;
        double r6367563 = r6367559 + r6367562;
        double r6367564 = a;
        double r6367565 = b;
        double r6367566 = r6367564 * r6367565;
        double r6367567 = r6367563 + r6367566;
        double r6367568 = c;
        double r6367569 = i;
        double r6367570 = r6367568 * r6367569;
        double r6367571 = r6367567 + r6367570;
        return r6367571;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r6367572 = i;
        double r6367573 = c;
        double r6367574 = a;
        double r6367575 = b;
        double r6367576 = x;
        double r6367577 = y;
        double r6367578 = t;
        double r6367579 = z;
        double r6367580 = r6367578 * r6367579;
        double r6367581 = fma(r6367576, r6367577, r6367580);
        double r6367582 = fma(r6367574, r6367575, r6367581);
        double r6367583 = fma(r6367572, r6367573, r6367582);
        return r6367583;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019120 +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)))