Average Error: 0.0 → 0.0
Time: 12.4s
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 r133152 = x;
        double r133153 = 1.0;
        double r133154 = r133152 + r133153;
        double r133155 = y;
        double r133156 = r133154 * r133155;
        double r133157 = r133156 - r133152;
        return r133157;
}
↓
double f(double x, double y) {
        double r133158 = x;
        double r133159 = 1.0;
        double r133160 = r133158 + r133159;
        double r133161 = y;
        double r133162 = -r133158;
        double r133163 = fma(r133160, r133161, r133162);
        return r133163;
}

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 2019322 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))