Average Error: 0.0 → 0
Time: 649.0ms
Precision: binary64
\[x \cdot y - x \]
↓
\[\mathsf{fma}\left(x, y, -x\right) \]
x \cdot y - x
↓
\mathsf{fma}\left(x, y, -x\right)

(FPCore (x y) :precision binary64 (- (* x y) x))
↓
(FPCore (x y) :precision binary64 (fma x y (- x)))
double code(double x, double y) {
	return (x * y) - x;
}
↓
double code(double x, double y) {
	return fma(x, y, -x);
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[x \cdot y - x \]

  2. Applied fma-neg_binary640

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2021275 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))