Average Error: 0.0 → 0.0
Time: 1.2s
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 r196955 = x;
        double r196956 = 1.0;
        double r196957 = r196955 + r196956;
        double r196958 = y;
        double r196959 = r196957 * r196958;
        double r196960 = r196959 - r196955;
        return r196960;
}
↓
double f(double x, double y) {
        double r196961 = x;
        double r196962 = 1.0;
        double r196963 = r196961 + r196962;
        double r196964 = y;
        double r196965 = -r196961;
        double r196966 = fma(r196963, r196964, r196965);
        return r196966;
}

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 2020002 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))