Average Error: 0.0 → 0.0
Time: 10.6s
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 r4200584 = x;
        double r4200585 = 1.0;
        double r4200586 = r4200585 - r4200584;
        double r4200587 = r4200584 / r4200586;
        return r4200587;
}
↓
double f(double x) {
        double r4200588 = x;
        double r4200589 = 1.0;
        double r4200590 = r4200589 - r4200588;
        double r4200591 = r4200588 / r4200590;
        return r4200591;
}

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-sqrt16.0

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

  4. Applied *-un-lft-identity16.0

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

  5. Applied times-frac16.0

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

  7. Applied frac-times16.0

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

  8. Simplified16.0

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

  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 
(FPCore (x)
  :name "Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1"
  (/ x (- 1.0 x)))