Average Error: 0.0 → 0.0
Time: 2.1s
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 r298493 = x;
        double r298494 = 1.0;
        double r298495 = r298493 + r298494;
        double r298496 = y;
        double r298497 = r298495 * r298496;
        double r298498 = r298497 - r298493;
        return r298498;
}
↓
double f(double x, double y) {
        double r298499 = x;
        double r298500 = 1.0;
        double r298501 = r298499 + r298500;
        double r298502 = y;
        double r298503 = -r298499;
        double r298504 = fma(r298501, r298502, r298503);
        return r298504;
}

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 2020057 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))