Average Error: 0.0 → 0
Time: 640.0ms
Precision: 64
\[x \cdot y - x\]
↓
\[\mathsf{fma}\left(y, x, -x\right)\]
x \cdot y - x
↓
\mathsf{fma}\left(y, x, -x\right)
double code(double x, double y) {
	return ((x * y) - x);
}
↓
double code(double x, double y) {
	return fma(y, x, -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 *-commutative0.0

    \[\leadsto \color{blue}{y \cdot x} - x\]

  4. Applied fma-neg0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))