Average Error: 14.8 → 0.1
Time: 13.1s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{1}{\frac{x}{-\sqrt{1}}}}{\frac{x + 1}{\sqrt{1}}}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{1}{\frac{x}{-\sqrt{1}}}}{\frac{x + 1}{\sqrt{1}}}
double f(double x) {
        double r38304 = 1.0;
        double r38305 = x;
        double r38306 = r38305 + r38304;
        double r38307 = r38304 / r38306;
        double r38308 = r38304 / r38305;
        double r38309 = r38307 - r38308;
        return r38309;
}
↓
double f(double x) {
        double r38310 = 1.0;
        double r38311 = x;
        double r38312 = sqrt(r38310);
        double r38313 = -r38312;
        double r38314 = r38311 / r38313;
        double r38315 = r38310 / r38314;
        double r38316 = r38311 + r38310;
        double r38317 = r38316 / r38312;
        double r38318 = r38315 / r38317;
        return r38318;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

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

  3. Applied frac-sub14.1

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

  4. Simplified14.1

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

  6. Applied associate-/r*14.1

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

  7. Simplified0.1

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

  9. Applied div-inv0.1

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

  10. Applied associate-/l*0.4

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

  11. Simplified0.3

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

  13. Applied add-sqr-sqrt0.3

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

  14. Applied distribute-lft-neg-in0.3

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

  15. Applied times-frac0.3

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

  16. Applied associate-/r*0.1

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

  17. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))