Average Error: 0.0 → 0.0
Time: 1.2s
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 r176566 = x;
        double r176567 = 1.0;
        double r176568 = r176566 + r176567;
        double r176569 = y;
        double r176570 = r176568 * r176569;
        double r176571 = r176570 - r176566;
        return r176571;
}
↓
double f(double x, double y) {
        double r176572 = x;
        double r176573 = 1.0;
        double r176574 = r176572 + r176573;
        double r176575 = y;
        double r176576 = -r176572;
        double r176577 = fma(r176574, r176575, r176576);
        return r176577;
}

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 2020018 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))