Average Error: 0.0 → 0
Time: 3.5s
Precision: 64
\[x \cdot y - x\]
↓
\[\mathsf{fma}\left(x, y, -x\right)\]
x \cdot y - x
↓
\mathsf{fma}\left(x, y, -x\right)
double f(double x, double y) {
        double r18413 = x;
        double r18414 = y;
        double r18415 = r18413 * r18414;
        double r18416 = r18415 - r18413;
        return r18416;
}
↓
double f(double x, double y) {
        double r18417 = x;
        double r18418 = y;
        double r18419 = -r18417;
        double r18420 = fma(r18417, r18418, r18419);
        return r18420;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[x \cdot y - x\]
  2. Using strategy rm

  3. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, -x\right)}\]

  4. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, y, -x\right)\]

Reproduce

herbie shell --seed 2019315 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))