Average Error: 0.0 → 0.0
Time: 1.6s
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 r223087 = 500.0;
        double r223088 = x;
        double r223089 = y;
        double r223090 = r223088 - r223089;
        double r223091 = r223087 * r223090;
        return r223091;
}
↓
double f(double x, double y) {
        double r223092 = 500.0;
        double r223093 = x;
        double r223094 = y;
        double r223095 = -r223094;
        double r223096 = r223092 * r223095;
        double r223097 = fma(r223092, r223093, r223096);
        return r223097;
}

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 2020039 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500 (- x y)))