Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[\left(x + 1\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(x + 1, y, -x\right)\]
\left(x + 1\right) \cdot y - x
↓
\mathsf{fma}\left(x + 1, y, -x\right)
double f(double x, double y) {
        double r144034 = x;
        double r144035 = 1.0;
        double r144036 = r144034 + r144035;
        double r144037 = y;
        double r144038 = r144036 * r144037;
        double r144039 = r144038 - r144034;
        return r144039;
}
↓
double f(double x, double y) {
        double r144040 = x;
        double r144041 = 1.0;
        double r144042 = r144040 + r144041;
        double r144043 = y;
        double r144044 = -r144040;
        double r144045 = fma(r144042, r144043, r144044);
        return r144045;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x + 1\right) \cdot y - x\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x + 1, y, -x\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x + 1, y, -x\right)\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))