Average Error: 0.0 → 0.0
Time: 20.5s
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 r11423588 = x;
        double r11423589 = 1.0;
        double r11423590 = r11423588 + r11423589;
        double r11423591 = y;
        double r11423592 = r11423590 * r11423591;
        double r11423593 = r11423592 - r11423588;
        return r11423593;
}
↓
double f(double x, double y) {
        double r11423594 = 1.0;
        double r11423595 = x;
        double r11423596 = r11423594 + r11423595;
        double r11423597 = y;
        double r11423598 = -r11423595;
        double r11423599 = fma(r11423596, r11423597, r11423598);
        return r11423599;
}

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 2019165 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))