Average Error: 0.0 → 0.0
Time: 9.9s
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 r2580551 = x;
        double r2580552 = y;
        double r2580553 = r2580551 * r2580552;
        double r2580554 = z;
        double r2580555 = t;
        double r2580556 = r2580554 * r2580555;
        double r2580557 = r2580553 + r2580556;
        double r2580558 = a;
        double r2580559 = b;
        double r2580560 = r2580558 * r2580559;
        double r2580561 = r2580557 + r2580560;
        double r2580562 = c;
        double r2580563 = i;
        double r2580564 = r2580562 * r2580563;
        double r2580565 = r2580561 + r2580564;
        return r2580565;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2580566 = z;
        double r2580567 = t;
        double r2580568 = x;
        double r2580569 = y;
        double r2580570 = c;
        double r2580571 = i;
        double r2580572 = b;
        double r2580573 = a;
        double r2580574 = r2580572 * r2580573;
        double r2580575 = fma(r2580570, r2580571, r2580574);
        double r2580576 = fma(r2580568, r2580569, r2580575);
        double r2580577 = fma(r2580566, r2580567, r2580576);
        return r2580577;
}

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 2019168 +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)))