Average Error: 0.0 → 0
Time: 4.8s
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 r10927919 = x;
        double r10927920 = y;
        double r10927921 = r10927919 * r10927920;
        double r10927922 = r10927921 - r10927919;
        return r10927922;
}
↓
double f(double x, double y) {
        double r10927923 = x;
        double r10927924 = y;
        double r10927925 = -r10927923;
        double r10927926 = fma(r10927923, r10927924, r10927925);
        return r10927926;
}

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 2019172 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))