Average Error: 0.1 → 0.1
Time: 4.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{1 \cdot m - {m}^{3}}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{1 \cdot m - {m}^{3}}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r16019 = m;
        double r16020 = 1.0;
        double r16021 = r16020 - r16019;
        double r16022 = r16019 * r16021;
        double r16023 = v;
        double r16024 = r16022 / r16023;
        double r16025 = r16024 - r16020;
        double r16026 = r16025 * r16021;
        return r16026;
}
↓
double f(double m, double v) {
        double r16027 = 1.0;
        double r16028 = m;
        double r16029 = r16027 * r16028;
        double r16030 = 3.0;
        double r16031 = pow(r16028, r16030);
        double r16032 = r16029 - r16031;
        double r16033 = v;
        double r16034 = r16027 + r16028;
        double r16035 = r16033 * r16034;
        double r16036 = r16032 / r16035;
        double r16037 = r16036 - r16027;
        double r16038 = r16027 - r16028;
        double r16039 = r16037 * r16038;
        return r16039;
}

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 flip--0.1

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

  4. Applied associate-*r/0.1

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

  5. Applied associate-/l/0.1

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

  6. Taylor expanded around 0 0.1

    \[\leadsto \left(\frac{\color{blue}{1 \cdot m - {m}^{3}}}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)\]

  7. Final simplification0.1

    \[\leadsto \left(\frac{1 \cdot m - {m}^{3}}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)\]

Reproduce

herbie shell --seed 2020049 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))