Average Error: 14.2 → 0.1
Time: 26.1s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x}}{x + 1}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x}}{x + 1}
double f(double x) {
        double r504209 = 1.0;
        double r504210 = x;
        double r504211 = r504210 + r504209;
        double r504212 = r504209 / r504211;
        double r504213 = r504209 / r504210;
        double r504214 = r504212 - r504213;
        return r504214;
}
↓
double f(double x) {
        double r504215 = -1.0;
        double r504216 = x;
        double r504217 = r504215 / r504216;
        double r504218 = 1.0;
        double r504219 = r504216 + r504218;
        double r504220 = r504217 / r504219;
        return r504220;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.2

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

  3. Applied frac-sub13.6

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

  4. Simplified0.4

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

  5. Simplified0.4

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

  7. Applied *-un-lft-identity0.4

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

  8. Applied distribute-rgt-out0.4

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

  9. Applied associate-/r*0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019144 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))