Average Error: 0.0 → 0.0
Time: 12.2s
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 r174945 = 200.0;
        double r174946 = x;
        double r174947 = y;
        double r174948 = r174946 - r174947;
        double r174949 = r174945 * r174948;
        return r174949;
}
↓
double f(double x, double y) {
        double r174950 = 200.0;
        double r174951 = x;
        double r174952 = y;
        double r174953 = -r174952;
        double r174954 = r174953 * r174950;
        double r174955 = fma(r174950, r174951, r174954);
        return r174955;
}

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)))