Average Error: 0.0 → 0.0
Time: 13.2s
Precision: 64
\[200 \cdot \left(x - y\right)\]
↓
\[\mathsf{fma}\left(200, x, \left(-y\right) \cdot 200\right)\]
200 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(200, x, \left(-y\right) \cdot 200\right)
double f(double x, double y) {
        double r167256 = 200.0;
        double r167257 = x;
        double r167258 = y;
        double r167259 = r167257 - r167258;
        double r167260 = r167256 * r167259;
        return r167260;
}
↓
double f(double x, double y) {
        double r167261 = 200.0;
        double r167262 = x;
        double r167263 = y;
        double r167264 = -r167263;
        double r167265 = r167264 * r167261;
        double r167266 = fma(r167261, r167262, r167265);
        return r167266;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[200 \cdot \left(x - y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto 200 \cdot \color{blue}{\left(x + \left(-y\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{200 \cdot x + 200 \cdot \left(-y\right)}\]

  5. Simplified0.0

    \[\leadsto 200 \cdot x + \color{blue}{\left(-y\right) \cdot 200}\]
  6. Using strategy rm

  7. Applied fma-def0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(200, x, \left(-y\right) \cdot 200\right)}\]

  8. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(200, x, \left(-y\right) \cdot 200\right)\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200 (- x y)))