Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[x \cdot y - x\]
↓
\[x \cdot \left(y - 1\right)\]
x \cdot y - x
↓
x \cdot \left(y - 1\right)
double f(double x, double y) {
        double r236455 = x;
        double r236456 = y;
        double r236457 = r236455 * r236456;
        double r236458 = r236457 - r236455;
        return r236458;
}
↓
double f(double x, double y) {
        double r236459 = x;
        double r236460 = y;
        double r236461 = 1.0;
        double r236462 = r236460 - r236461;
        double r236463 = r236459 * r236462;
        return r236463;
}

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--29.0

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

  4. Simplified31.4

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

  6. Applied *-un-lft-identity31.4

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

  7. Applied times-frac9.5

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

  8. Simplified9.5

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

  9. Taylor expanded around 0 0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))