Average Error: 0.0 → 0.0
Time: 9.7s
Precision: 64
\[500 \cdot \left(x - y\right)\]
↓
\[\mathsf{fma}\left(500, x, 500 \cdot \left(-y\right)\right)\]
500 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(500, x, 500 \cdot \left(-y\right)\right)
double f(double x, double y) {
        double r158235 = 500.0;
        double r158236 = x;
        double r158237 = y;
        double r158238 = r158236 - r158237;
        double r158239 = r158235 * r158238;
        return r158239;
}
↓
double f(double x, double y) {
        double r158240 = 500.0;
        double r158241 = x;
        double r158242 = y;
        double r158243 = -r158242;
        double r158244 = r158240 * r158243;
        double r158245 = fma(r158240, r158241, r158244);
        return r158245;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[500 \cdot \left(x - y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto 500 \cdot \color{blue}{\left(x + \left(-y\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{500 \cdot x + 500 \cdot \left(-y\right)}\]
  5. Using strategy rm

  6. Applied fma-def0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(500, x, 500 \cdot \left(-y\right)\right)}\]

  7. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(500, x, 500 \cdot \left(-y\right)\right)\]

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500 (- x y)))