Average Error: 0.1 → 0.1
Time: 26.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\left(-1\right) + \frac{m}{\left(m + 1\right) \cdot \frac{\frac{v}{m + 1}}{1 - m}}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\left(-1\right) + \frac{m}{\left(m + 1\right) \cdot \frac{\frac{v}{m + 1}}{1 - m}}\right)
double f(double m, double v) {
        double r1197016 = m;
        double r1197017 = 1.0;
        double r1197018 = r1197017 - r1197016;
        double r1197019 = r1197016 * r1197018;
        double r1197020 = v;
        double r1197021 = r1197019 / r1197020;
        double r1197022 = r1197021 - r1197017;
        double r1197023 = r1197022 * r1197018;
        return r1197023;
}
↓
double f(double m, double v) {
        double r1197024 = 1.0;
        double r1197025 = m;
        double r1197026 = r1197024 - r1197025;
        double r1197027 = -r1197024;
        double r1197028 = r1197025 + r1197024;
        double r1197029 = v;
        double r1197030 = r1197029 / r1197028;
        double r1197031 = r1197030 / r1197026;
        double r1197032 = r1197028 * r1197031;
        double r1197033 = r1197025 / r1197032;
        double r1197034 = r1197027 + r1197033;
        double r1197035 = r1197026 * r1197034;
        return r1197035;
}

Error

Bits error versus m

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \left(\color{blue}{\frac{m}{\frac{v}{1 - m}}} - 1\right) \cdot \left(1 - m\right)\]
  4. Using strategy rm

  5. Applied sub-neg0.1

    \[\leadsto \color{blue}{\left(\frac{m}{\frac{v}{1 - m}} + \left(-1\right)\right)} \cdot \left(1 - m\right)\]
  6. Using strategy rm

  7. Applied flip--0.1

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

  8. Applied associate-/r/0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))