Average Error: 0.0 → 0.0
Time: 8.6s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(x + 1\right) + \frac{1}{\frac{x + 1}{x}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(x + 1\right) + \frac{1}{\frac{x + 1}{x}}
double f(double x) {
        double r5405368 = 1.0;
        double r5405369 = x;
        double r5405370 = r5405369 - r5405368;
        double r5405371 = r5405368 / r5405370;
        double r5405372 = r5405369 + r5405368;
        double r5405373 = r5405369 / r5405372;
        double r5405374 = r5405371 + r5405373;
        return r5405374;
}
↓
double f(double x) {
        double r5405375 = 1.0;
        double r5405376 = x;
        double r5405377 = r5405376 * r5405376;
        double r5405378 = r5405375 * r5405375;
        double r5405379 = r5405377 - r5405378;
        double r5405380 = r5405375 / r5405379;
        double r5405381 = r5405376 + r5405375;
        double r5405382 = r5405380 * r5405381;
        double r5405383 = 1.0;
        double r5405384 = r5405381 / r5405376;
        double r5405385 = r5405383 / r5405384;
        double r5405386 = r5405382 + r5405385;
        return r5405386;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied clear-num0.0

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

  5. Applied flip--0.0

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

  6. Applied associate-/r/0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))