Average Error: 14.4 → 0.1
Time: 2.9s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{1}{\frac{x}{\sqrt[3]{0 - 1} \cdot \sqrt[3]{0 - 1}}}}{\frac{x + 1}{\sqrt[3]{0 - 1}}}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{1}{\frac{x}{\sqrt[3]{0 - 1} \cdot \sqrt[3]{0 - 1}}}}{\frac{x + 1}{\sqrt[3]{0 - 1}}}
double f(double x) {
        double r29927 = 1.0;
        double r29928 = x;
        double r29929 = r29928 + r29927;
        double r29930 = r29927 / r29929;
        double r29931 = r29927 / r29928;
        double r29932 = r29930 - r29931;
        return r29932;
}
↓
double f(double x) {
        double r29933 = 1.0;
        double r29934 = x;
        double r29935 = 0.0;
        double r29936 = r29935 - r29933;
        double r29937 = cbrt(r29936);
        double r29938 = r29937 * r29937;
        double r29939 = r29934 / r29938;
        double r29940 = r29933 / r29939;
        double r29941 = r29934 + r29933;
        double r29942 = r29941 / r29937;
        double r29943 = r29940 / r29942;
        return r29943;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  2. Using strategy rm

  3. Applied frac-sub13.9

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

  4. Simplified13.9

    \[\leadsto \frac{\color{blue}{1 \cdot \left(x - \left(x + 1\right)\right)}}{\left(x + 1\right) \cdot x}\]
  5. Using strategy rm

  6. Applied associate-/r*13.9

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

  7. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{1}{\frac{x + 1}{0 - 1}}}}{x}\]
  8. Using strategy rm

  9. Applied div-inv0.1

    \[\leadsto \frac{\color{blue}{1 \cdot \frac{1}{\frac{x + 1}{0 - 1}}}}{x}\]

  10. Applied associate-/l*0.4

    \[\leadsto \color{blue}{\frac{1}{\frac{x}{\frac{1}{\frac{x + 1}{0 - 1}}}}}\]

  11. Simplified0.4

    \[\leadsto \frac{1}{\color{blue}{\frac{x \cdot \left(x + 1\right)}{0 - 1}}}\]
  12. Using strategy rm

  13. Applied add-cube-cbrt0.4

    \[\leadsto \frac{1}{\frac{x \cdot \left(x + 1\right)}{\color{blue}{\left(\sqrt[3]{0 - 1} \cdot \sqrt[3]{0 - 1}\right) \cdot \sqrt[3]{0 - 1}}}}\]

  14. Applied times-frac0.4

    \[\leadsto \frac{1}{\color{blue}{\frac{x}{\sqrt[3]{0 - 1} \cdot \sqrt[3]{0 - 1}} \cdot \frac{x + 1}{\sqrt[3]{0 - 1}}}}\]

  15. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{1}{\frac{x}{\sqrt[3]{0 - 1} \cdot \sqrt[3]{0 - 1}}}}{\frac{x + 1}{\sqrt[3]{0 - 1}}}}\]

  16. Final simplification0.1

    \[\leadsto \frac{\frac{1}{\frac{x}{\sqrt[3]{0 - 1} \cdot \sqrt[3]{0 - 1}}}}{\frac{x + 1}{\sqrt[3]{0 - 1}}}\]

Reproduce

herbie shell --seed 2019356 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))