Average Error: 14.2 → 0.1
Time: 36.3s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{-2}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{-2}{x + 1}}{x - 1}
double f(double x) {
        double r3665941 = 1.0;
        double r3665942 = x;
        double r3665943 = r3665942 + r3665941;
        double r3665944 = r3665941 / r3665943;
        double r3665945 = r3665942 - r3665941;
        double r3665946 = r3665941 / r3665945;
        double r3665947 = r3665944 - r3665946;
        return r3665947;
}
↓
double f(double x) {
        double r3665948 = -2.0;
        double r3665949 = x;
        double r3665950 = 1.0;
        double r3665951 = r3665949 + r3665950;
        double r3665952 = r3665948 / r3665951;
        double r3665953 = r3665949 - r3665950;
        double r3665954 = r3665952 / r3665953;
        return r3665954;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 14.2

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

  3. Applied frac-sub13.7

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

  4. Simplified0.4

    \[\leadsto \frac{\color{blue}{-2}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]

  5. Simplified0.4

    \[\leadsto \frac{-2}{\color{blue}{x \cdot x - 1}}\]
  6. Using strategy rm

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

    \[\leadsto \frac{-2}{x \cdot x - \color{blue}{1 \cdot 1}}\]

  8. Applied difference-of-squares0.4

    \[\leadsto \frac{-2}{\color{blue}{\left(x + 1\right) \cdot \left(x - 1\right)}}\]

  9. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{-2}{x + 1}}{x - 1}}\]

  10. Final simplification0.1

    \[\leadsto \frac{\frac{-2}{x + 1}}{x - 1}\]

Reproduce

herbie shell --seed 2019144 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))