Average Error: 0.0 → 0.0
Time: 29.2s
Precision: 64
\[\frac{x}{1.0 - x}\]
↓
\[\frac{x}{1.0 - x}\]
\frac{x}{1.0 - x}
↓
\frac{x}{1.0 - x}
double f(double x) {
        double r8055332 = x;
        double r8055333 = 1.0;
        double r8055334 = r8055333 - r8055332;
        double r8055335 = r8055332 / r8055334;
        return r8055335;
}
↓
double f(double x) {
        double r8055336 = x;
        double r8055337 = 1.0;
        double r8055338 = r8055337 - r8055336;
        double r8055339 = r8055336 / r8055338;
        return r8055339;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{x}{1.0 - x}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt16.1

    \[\leadsto \frac{x}{\color{blue}{\sqrt{1.0 - x} \cdot \sqrt{1.0 - x}}}\]

  4. Applied *-un-lft-identity16.1

    \[\leadsto \frac{\color{blue}{1 \cdot x}}{\sqrt{1.0 - x} \cdot \sqrt{1.0 - x}}\]

  5. Applied times-frac16.1

    \[\leadsto \color{blue}{\frac{1}{\sqrt{1.0 - x}} \cdot \frac{x}{\sqrt{1.0 - x}}}\]
  6. Using strategy rm

  7. Applied frac-times16.1

    \[\leadsto \color{blue}{\frac{1 \cdot x}{\sqrt{1.0 - x} \cdot \sqrt{1.0 - x}}}\]

  8. Simplified16.1

    \[\leadsto \frac{\color{blue}{x}}{\sqrt{1.0 - x} \cdot \sqrt{1.0 - x}}\]

  9. Simplified0.0

    \[\leadsto \frac{x}{\color{blue}{1.0 - x}}\]

  10. Final simplification0.0

    \[\leadsto \frac{x}{1.0 - x}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x)
  :name "Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1"
  (/ x (- 1.0 x)))