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

Average Error: 0.0 → 0

Time: 2.8s

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 r242611 = x;
        double r242612 = y;
        double r242613 = r242611 * r242612;
        double r242614 = r242613 - r242611;
        return r242614;
}

↓

double f(double x, double y) {
        double r242615 = x;
        double r242616 = y;
        double r242617 = -r242615;
        double r242618 = fma(r242615, r242616, r242617);
        return r242618;
}

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 2020042 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))