Average Error: 0.1 → 0.1
Time: 3.6s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{\frac{v}{1 \cdot 1 - m \cdot m} \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{\frac{v}{1 \cdot 1 - m \cdot m} \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r11204 = m;
        double r11205 = 1.0;
        double r11206 = r11205 - r11204;
        double r11207 = r11204 * r11206;
        double r11208 = v;
        double r11209 = r11207 / r11208;
        double r11210 = r11209 - r11205;
        double r11211 = r11210 * r11206;
        return r11211;
}
↓
double f(double m, double v) {
        double r11212 = m;
        double r11213 = v;
        double r11214 = 1.0;
        double r11215 = r11214 * r11214;
        double r11216 = r11212 * r11212;
        double r11217 = r11215 - r11216;
        double r11218 = r11213 / r11217;
        double r11219 = r11214 + r11212;
        double r11220 = r11218 * r11219;
        double r11221 = r11212 / r11220;
        double r11222 = r11221 - r11214;
        double r11223 = r11214 - r11212;
        double r11224 = r11222 * r11223;
        return r11224;
}

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 flip--0.1

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

  6. Applied associate-/r/0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(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)))