Average Error: 0.0 → 0.0
Time: 7.5s
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 r13731847 = x;
        double r13731848 = 1.0;
        double r13731849 = r13731847 + r13731848;
        double r13731850 = y;
        double r13731851 = r13731849 * r13731850;
        double r13731852 = r13731851 - r13731847;
        return r13731852;
}
↓
double f(double x, double y) {
        double r13731853 = x;
        double r13731854 = 1.0;
        double r13731855 = r13731853 + r13731854;
        double r13731856 = y;
        double r13731857 = -r13731853;
        double r13731858 = fma(r13731855, r13731856, r13731857);
        return r13731858;
}

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 2019174 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))