Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1

Average Error: 0.0 → 0

Time: 2.6s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x \cdot y - x\]

↓

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

C

double f(double x, double y) {
        double r231080 = x;
        double r231081 = y;
        double r231082 = r231080 * r231081;
        double r231083 = r231082 - r231080;
        return r231083;
}

↓

double f(double x, double y) {
        double r231084 = x;
        double r231085 = y;
        double r231086 = -r231084;
        double r231087 = fma(r231084, r231085, r231086);
        return r231087;
}

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-neg 0

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

4. Final simplification 0

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))