Average Error: 0.1 → 0.1
Time: 22.5min
Precision: binary64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \left(m \cdot 1 + \frac{\frac{m \cdot \left(m - 1\right)}{v}}{\frac{1}{m}}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \left(m \cdot 1 + \frac{\frac{m \cdot \left(m - 1\right)}{v}}{\frac{1}{m}}\right)
double code(double m, double v) {
	return ((double) (((double) ((((double) (m * ((double) (1.0 - m)))) / v) - 1.0)) * ((double) (1.0 - m))));
}
↓
double code(double m, double v) {
	return ((double) (((double) (((double) ((((double) (m * ((double) (1.0 - m)))) / v) - 1.0)) * 1.0)) + ((double) (((double) (m * 1.0)) + ((((double) (m * ((double) (m - 1.0)))) / v) / (1.0 / 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

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

  4. Applied distribute-lft-in0.1

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

  5. Simplified0.1

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

  7. Applied sub-neg0.1

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

  8. Applied distribute-lft-in0.1

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

  9. Simplified0.1

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

  11. Applied div-inv0.1

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

  12. Applied associate-/r*0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2020181 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))