Average Error: 0.2 → 0.2
Time: 7.3s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\frac{m}{v} - \left(\frac{m \cdot m}{v} + 1\right)\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(\frac{m}{v} - \left(\frac{m \cdot m}{v} + 1\right)\right)
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v) :precision binary64 (* m (- (/ m v) (+ (/ (* m m) v) 1.0))))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * m;
}
↓
double code(double m, double v) {
	return m * ((m / v) - (((m * m) / v) + 1.0));
}

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 0.2

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
  2. Using strategy rm

  3. Applied sub-neg_binary64_7530.2

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

  4. Applied distribute-rgt-in_binary64_7100.2

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

  5. Simplified0.2

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

  6. Simplified0.2

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

  8. Applied distribute-rgt-neg-out_binary64_7200.2

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

  9. Applied unsub-neg_binary64_7540.2

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

  10. Applied div-sub_binary64_7650.2

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

  11. Applied associate--l-_binary64_6980.2

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

  12. Final simplification0.2

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

Alternatives

Reproduce

herbie shell --seed 2021100 
(FPCore (m v)
  :name "a 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) m))