Average Error: 0.0 → 0.0
Time: 1.0s
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 r305993 = 500.0;
        double r305994 = x;
        double r305995 = y;
        double r305996 = r305994 - r305995;
        double r305997 = r305993 * r305996;
        return r305997;
}
↓
double f(double x, double y) {
        double r305998 = 500.0;
        double r305999 = x;
        double r306000 = y;
        double r306001 = -r306000;
        double r306002 = r305998 * r306001;
        double r306003 = fma(r305998, r305999, r306002);
        return r306003;
}

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 2020035 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500 (- x y)))