Average Error: 0.0 → 0
Time: 604.0ms
Precision: 64
\[x \cdot y - x\]
↓
\[\mathsf{fma}\left(x \cdot 1, y, -x\right)\]
x \cdot y - x
↓
\mathsf{fma}\left(x \cdot 1, y, -x\right)
double code(double x, double y) {
	return ((double) (((double) (x * y)) - x));
}
↓
double code(double x, double y) {
	return ((double) fma(((double) (x * 1.0)), y, ((double) -(x))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied *-un-lft-identity0.0

    \[\leadsto x \cdot \color{blue}{\left(1 \cdot y\right)} - x\]

  4. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(x \cdot 1\right) \cdot y} - x\]

  5. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot 1, y, -x\right)}\]

  6. Final simplification0

    \[\leadsto \mathsf{fma}\left(x \cdot 1, y, -x\right)\]

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))