Average Error: 0.1 → 0.1
Time: 4.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{1 \cdot m + \left(-m\right) \cdot m}{v} - 1\right) \cdot 1 + \left(\left(-1\right) + \frac{1}{\frac{v}{1 \cdot 1 - m \cdot m}} \cdot \frac{m}{1 + m}\right) \cdot \left(-m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{1 \cdot m + \left(-m\right) \cdot m}{v} - 1\right) \cdot 1 + \left(\left(-1\right) + \frac{1}{\frac{v}{1 \cdot 1 - m \cdot m}} \cdot \frac{m}{1 + m}\right) \cdot \left(-m\right)
double code(double m, double v) {
	return ((((m * (1.0 - m)) / v) - 1.0) * (1.0 - m));
}
↓
double code(double m, double v) {
	return ((((((1.0 * m) + (-m * m)) / v) - 1.0) * 1.0) + ((-1.0 + ((1.0 / (v / ((1.0 * 1.0) - (m * m)))) * (m / (1.0 + m)))) * -m));
}

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 sub-neg0.1

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

  9. Applied distribute-lft-in0.1

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

  10. Simplified0.1

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

  12. Applied flip--0.1

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

  13. Applied associate-/r/0.1

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

  14. Applied *-un-lft-identity0.1

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

  15. Applied times-frac0.1

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

  16. Final simplification0.1

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

Reproduce

herbie shell --seed 2020066 
(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)))