Average Error: 0.0 → 0.0
Time: 9.9s
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 r8681104 = x;
        double r8681105 = 1.0;
        double r8681106 = r8681104 + r8681105;
        double r8681107 = y;
        double r8681108 = r8681106 * r8681107;
        double r8681109 = r8681108 - r8681104;
        return r8681109;
}
↓
double f(double x, double y) {
        double r8681110 = 1.0;
        double r8681111 = x;
        double r8681112 = r8681110 + r8681111;
        double r8681113 = y;
        double r8681114 = -r8681111;
        double r8681115 = fma(r8681112, r8681113, r8681114);
        return r8681115;
}

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))