Average Error: 0.0 → 0.0
Time: 6.6s
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 r22201 = x;
        double r22202 = 1.0;
        double r22203 = r22201 + r22202;
        double r22204 = y;
        double r22205 = r22203 * r22204;
        double r22206 = r22205 - r22201;
        return r22206;
}
↓
double f(double x, double y) {
        double r22207 = x;
        double r22208 = 1.0;
        double r22209 = r22207 + r22208;
        double r22210 = y;
        double r22211 = -r22207;
        double r22212 = fma(r22209, r22210, r22211);
        return r22212;
}

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 2019310 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))