Average Error: 0.0 → 0.0
Time: 7.8s
Precision: 64
\[500 \cdot \left(x - y\right)\]
↓
\[\mathsf{fma}\left(x, 500, \left(-y\right) \cdot 500\right)\]
500 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(x, 500, \left(-y\right) \cdot 500\right)
double f(double x, double y) {
        double r255679 = 500.0;
        double r255680 = x;
        double r255681 = y;
        double r255682 = r255680 - r255681;
        double r255683 = r255679 * r255682;
        return r255683;
}
↓
double f(double x, double y) {
        double r255684 = x;
        double r255685 = 500.0;
        double r255686 = y;
        double r255687 = -r255686;
        double r255688 = r255687 * r255685;
        double r255689 = fma(r255684, r255685, r255688);
        return r255689;
}

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. Simplified0.0

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

  6. Simplified0.0

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

  8. Applied fma-def0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500 (- x y)))