Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[0.5 \cdot \left(x \cdot x - y\right)\]
↓
\[\mathsf{fma}\left(x, x, -y\right) \cdot 0.5\]
0.5 \cdot \left(x \cdot x - y\right)
↓
\mathsf{fma}\left(x, x, -y\right) \cdot 0.5
double f(double x, double y) {
        double r8065 = 0.5;
        double r8066 = x;
        double r8067 = r8066 * r8066;
        double r8068 = y;
        double r8069 = r8067 - r8068;
        double r8070 = r8065 * r8069;
        return r8070;
}
↓
double f(double x, double y) {
        double r8071 = x;
        double r8072 = y;
        double r8073 = -r8072;
        double r8074 = fma(r8071, r8071, r8073);
        double r8075 = 0.5;
        double r8076 = r8074 * r8075;
        return r8076;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[0.5 \cdot \left(x \cdot x - y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, -y\right) \cdot 0.5}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, x, -y\right) \cdot 0.5\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  (* 0.5 (- (* x x) y)))