Average Error: 0.0 → 0.0
Time: 880.0ms
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 r217590 = x;
        double r217591 = 1.0;
        double r217592 = r217590 + r217591;
        double r217593 = y;
        double r217594 = r217592 * r217593;
        double r217595 = r217594 - r217590;
        return r217595;
}
↓
double f(double x, double y) {
        double r217596 = x;
        double r217597 = 1.0;
        double r217598 = r217596 + r217597;
        double r217599 = y;
        double r217600 = -r217596;
        double r217601 = fma(r217598, r217599, r217600);
        return r217601;
}

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 2020001 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))