Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
\[x \cdot y - x\]
↓
\[x \cdot \left(y + -1\right)\]
x \cdot y - x
↓
x \cdot \left(y + -1\right)
(FPCore (x y) :precision binary64 (- (* x y) x))
↓
(FPCore (x y) :precision binary64 (* x (+ y -1.0)))
double code(double x, double y) {
	return (x * y) - x;
}
↓
double code(double x, double y) {
	return x * (y + -1.0);
}

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 flip--_binary64_755528.5

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

  4. Simplified36.0

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

  5. Simplified36.0

    \[\leadsto \frac{x \cdot \left(x \cdot \left(y \cdot y\right) - x\right)}{\color{blue}{x + x \cdot y}}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity_binary64_758036.0

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

  8. Applied times-frac_binary64_758614.3

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

  9. Simplified14.3

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

  10. Taylor expanded around 0 0.0

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

  11. Simplified0.0

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

  12. Final simplification0.0

    \[\leadsto x \cdot \left(y + -1\right)\]

Reproduce

herbie shell --seed 2020355 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))