Average Error: 0.0 → 0.0
Time: 1.3s
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 r214001 = 500.0;
        double r214002 = x;
        double r214003 = y;
        double r214004 = r214002 - r214003;
        double r214005 = r214001 * r214004;
        return r214005;
}
↓
double f(double x, double y) {
        double r214006 = 500.0;
        double r214007 = x;
        double r214008 = y;
        double r214009 = -r214008;
        double r214010 = r214006 * r214009;
        double r214011 = fma(r214006, r214007, r214010);
        return r214011;
}

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 2019353 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500 (- x y)))