Average Error: 0.0 → 0.0
Time: 10.9s
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 r142529 = x;
        double r142530 = 1.0;
        double r142531 = r142529 + r142530;
        double r142532 = y;
        double r142533 = r142531 * r142532;
        double r142534 = r142533 - r142529;
        return r142534;
}
↓
double f(double x, double y) {
        double r142535 = x;
        double r142536 = 1.0;
        double r142537 = r142535 + r142536;
        double r142538 = y;
        double r142539 = -r142535;
        double r142540 = fma(r142537, r142538, r142539);
        return r142540;
}

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 2019305 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))