Average Error: 0.0 → 0.0
Time: 8.6s
Precision: 64
\[x \cdot y - x\]
↓
\[\left(y + -1\right) \cdot x\]
x \cdot y - x
↓
\left(y + -1\right) \cdot x
double f(double x, double y) {
        double r195781 = x;
        double r195782 = y;
        double r195783 = r195781 * r195782;
        double r195784 = r195783 - r195781;
        return r195784;
}
↓
double f(double x, double y) {
        double r195785 = y;
        double r195786 = -1.0;
        double r195787 = r195785 + r195786;
        double r195788 = x;
        double r195789 = r195787 * r195788;
        return r195789;
}

Error

Bits error versus x

Bits error versus y

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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 add-sqr-sqrt31.6

    \[\leadsto \color{blue}{\sqrt{x \cdot y - x} \cdot \sqrt{x \cdot y - x}}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube40.7

    \[\leadsto \sqrt{x \cdot y - x} \cdot \color{blue}{\sqrt[3]{\left(\sqrt{x \cdot y - x} \cdot \sqrt{x \cdot y - x}\right) \cdot \sqrt{x \cdot y - x}}}\]

  6. Applied add-cbrt-cube40.9

    \[\leadsto \color{blue}{\sqrt[3]{\left(\sqrt{x \cdot y - x} \cdot \sqrt{x \cdot y - x}\right) \cdot \sqrt{x \cdot y - x}}} \cdot \sqrt[3]{\left(\sqrt{x \cdot y - x} \cdot \sqrt{x \cdot y - x}\right) \cdot \sqrt{x \cdot y - x}}\]

  7. Applied cbrt-unprod51.6

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\sqrt{x \cdot y - x} \cdot \sqrt{x \cdot y - x}\right) \cdot \sqrt{x \cdot y - x}\right) \cdot \left(\left(\sqrt{x \cdot y - x} \cdot \sqrt{x \cdot y - x}\right) \cdot \sqrt{x \cdot y - x}\right)}}\]

  8. Simplified39.3

    \[\leadsto \sqrt[3]{\color{blue}{{\left(y \cdot x - x\right)}^{3}}}\]
  9. Using strategy rm

  10. Applied *-un-lft-identity39.3

    \[\leadsto \sqrt[3]{{\left(y \cdot x - \color{blue}{1 \cdot x}\right)}^{3}}\]

  11. Applied distribute-rgt-out--39.3

    \[\leadsto \sqrt[3]{{\color{blue}{\left(x \cdot \left(y - 1\right)\right)}}^{3}}\]

  12. Applied unpow-prod-down47.5

    \[\leadsto \sqrt[3]{\color{blue}{{x}^{3} \cdot {\left(y - 1\right)}^{3}}}\]

  13. Applied cbrt-prod46.6

    \[\leadsto \color{blue}{\sqrt[3]{{x}^{3}} \cdot \sqrt[3]{{\left(y - 1\right)}^{3}}}\]

  14. Simplified16.5

    \[\leadsto \color{blue}{x} \cdot \sqrt[3]{{\left(y - 1\right)}^{3}}\]

  15. Simplified0.0

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

  16. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))