Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[\left(x + 1\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(x + 1, y, -x\right)\]
\left(x + 1\right) \cdot y - x
↓
\mathsf{fma}\left(x + 1, y, -x\right)
double f(double x, double y) {
        double r207962 = x;
        double r207963 = 1.0;
        double r207964 = r207962 + r207963;
        double r207965 = y;
        double r207966 = r207964 * r207965;
        double r207967 = r207966 - r207962;
        return r207967;
}
↓
double f(double x, double y) {
        double r207968 = x;
        double r207969 = 1.0;
        double r207970 = r207968 + r207969;
        double r207971 = y;
        double r207972 = -r207968;
        double r207973 = fma(r207970, r207971, r207972);
        return r207973;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x + 1\right) \cdot y - x\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x + 1, y, -x\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x + 1, y, -x\right)\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))