Average Error: 0.1 → 0.1
Time: 22.8s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{v} \cdot \frac{1 \cdot 1 - m \cdot m}{1 + m} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{v} \cdot \frac{1 \cdot 1 - m \cdot m}{1 + m} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r24030 = m;
        double r24031 = 1.0;
        double r24032 = r24031 - r24030;
        double r24033 = r24030 * r24032;
        double r24034 = v;
        double r24035 = r24033 / r24034;
        double r24036 = r24035 - r24031;
        double r24037 = r24036 * r24032;
        return r24037;
}
↓
double f(double m, double v) {
        double r24038 = m;
        double r24039 = v;
        double r24040 = r24038 / r24039;
        double r24041 = 1.0;
        double r24042 = r24041 * r24041;
        double r24043 = r24038 * r24038;
        double r24044 = r24042 - r24043;
        double r24045 = r24041 + r24038;
        double r24046 = r24044 / r24045;
        double r24047 = r24040 * r24046;
        double r24048 = r24047 - r24041;
        double r24049 = r24041 - r24038;
        double r24050 = r24048 * r24049;
        return r24050;
}

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. Using strategy rm

  7. Applied times-frac0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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)))