Average Error: 0.1 → 0.1
Time: 16.6s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[\left(x \cdot \left(1 - y\right)\right) \cdot y\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
\left(x \cdot \left(1 - y\right)\right) \cdot y
double f(double x, double y) {
        double r24003 = x;
        double r24004 = y;
        double r24005 = r24003 * r24004;
        double r24006 = 1.0;
        double r24007 = r24006 - r24004;
        double r24008 = r24005 * r24007;
        return r24008;
}
↓
double f(double x, double y) {
        double r24009 = x;
        double r24010 = 1.0;
        double r24011 = y;
        double r24012 = r24010 - r24011;
        double r24013 = r24009 * r24012;
        double r24014 = r24013 * r24011;
        return r24014;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
  2. Using strategy rm

  3. Applied pow10.1

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

  4. Applied pow10.1

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

  5. Applied pow10.1

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

  6. Applied pow-prod-down0.1

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

  7. Applied pow-prod-down0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

    \[\leadsto \left(x \cdot \left(1 - y\right)\right) \cdot y\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))