Average Error: 0.1 → 0.1
Time: 6.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\frac{m}{\frac{v}{1 \cdot 1 - m \cdot m}}}{1 + m} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\frac{m}{\frac{v}{1 \cdot 1 - m \cdot m}}}{1 + m} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r17144 = m;
        double r17145 = 1.0;
        double r17146 = r17145 - r17144;
        double r17147 = r17144 * r17146;
        double r17148 = v;
        double r17149 = r17147 / r17148;
        double r17150 = r17149 - r17145;
        double r17151 = r17150 * r17146;
        return r17151;
}
↓
double f(double m, double v) {
        double r17152 = m;
        double r17153 = v;
        double r17154 = 1.0;
        double r17155 = r17154 * r17154;
        double r17156 = r17152 * r17152;
        double r17157 = r17155 - r17156;
        double r17158 = r17153 / r17157;
        double r17159 = r17152 / r17158;
        double r17160 = r17154 + r17152;
        double r17161 = r17159 / r17160;
        double r17162 = r17161 - r17154;
        double r17163 = r17154 - r17152;
        double r17164 = r17162 * r17163;
        return r17164;
}

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 sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Simplified0.1

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

  6. Simplified0.1

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

  8. Applied distribute-rgt-out0.1

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

  9. Applied associate-/l*0.1

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

  10. Simplified0.1

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

  12. Applied flip--0.1

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

  13. Applied associate-/r/0.1

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

  14. Applied associate-/r*0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2019354 +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)))