Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[500 \cdot \left(x - y\right)\]
↓
\[\mathsf{fma}\left(500, x, \left(-y\right) \cdot 500\right)\]
500 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(500, x, \left(-y\right) \cdot 500\right)
double f(double x, double y) {
        double r121093 = 500.0;
        double r121094 = x;
        double r121095 = y;
        double r121096 = r121094 - r121095;
        double r121097 = r121093 * r121096;
        return r121097;
}
↓
double f(double x, double y) {
        double r121098 = 500.0;
        double r121099 = x;
        double r121100 = y;
        double r121101 = -r121100;
        double r121102 = r121101 * r121098;
        double r121103 = fma(r121098, r121099, r121102);
        return r121103;
}

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

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

  7. Applied fma-def0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500 (- x y)))