Average Error: 0.0 → 0.0
Time: 26.8s
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 r6252002 = x;
        double r6252003 = 1.0;
        double r6252004 = r6252003 - r6252002;
        double r6252005 = r6252002 / r6252004;
        return r6252005;
}
↓
double f(double x) {
        double r6252006 = x;
        double r6252007 = 1.0;
        double r6252008 = r6252007 - r6252006;
        double r6252009 = r6252006 / r6252008;
        return r6252009;
}

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