Average Error: 14.6 → 0.4
Time: 24.4s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{-2}{-1 + x \cdot x}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{-2}{-1 + x \cdot x}
double f(double x) {
        double r3683179 = 1.0;
        double r3683180 = x;
        double r3683181 = r3683180 + r3683179;
        double r3683182 = r3683179 / r3683181;
        double r3683183 = r3683180 - r3683179;
        double r3683184 = r3683179 / r3683183;
        double r3683185 = r3683182 - r3683184;
        return r3683185;
}
↓
double f(double x) {
        double r3683186 = -2.0;
        double r3683187 = -1.0;
        double r3683188 = x;
        double r3683189 = r3683188 * r3683188;
        double r3683190 = r3683187 + r3683189;
        double r3683191 = r3683186 / r3683190;
        return r3683191;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.6

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

  3. Applied frac-sub13.9

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

  4. Simplified13.9

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

  5. Simplified13.9

    \[\leadsto \frac{\left(x + -2\right) - x}{\color{blue}{-1 + x \cdot x}}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity13.9

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

  8. Applied associate-/r*13.9

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

  9. Simplified0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019152 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))