Average Error: 0.0 → 0.0
Time: 9.3s
Precision: 64
\[\left(x + 1.0\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(1.0 + x, y, -x\right)\]
\left(x + 1.0\right) \cdot y - x
↓
\mathsf{fma}\left(1.0 + x, y, -x\right)
double f(double x, double y) {
        double r8631210 = x;
        double r8631211 = 1.0;
        double r8631212 = r8631210 + r8631211;
        double r8631213 = y;
        double r8631214 = r8631212 * r8631213;
        double r8631215 = r8631214 - r8631210;
        return r8631215;
}
↓
double f(double x, double y) {
        double r8631216 = 1.0;
        double r8631217 = x;
        double r8631218 = r8631216 + r8631217;
        double r8631219 = y;
        double r8631220 = -r8631217;
        double r8631221 = fma(r8631218, r8631219, r8631220);
        return r8631221;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x + 1.0\right) \cdot y - x\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x + 1.0, y, -x\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(1.0 + x, y, -x\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))