Average Error: 0.1 → 0.1
Time: 3.5s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right) \]
↓
\[\left(\frac{m - {m}^{2}}{v} - 1\right) \cdot \left(1 - m\right) \]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m - {m}^{2}}{v} - 1\right) \cdot \left(1 - m\right)

(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))
↓
(FPCore (m v)
 :precision binary64
 (* (- (/ (- m (pow m 2.0)) v) 1.0) (- 1.0 m)))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m);
}
↓
double code(double m, double v) {
	return (((m - pow(m, 2.0)) / v) - 1.0) * (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. Taylor expanded in v around inf 0.1

    \[\leadsto \left(\color{blue}{\frac{m - {m}^{2}}{v}} - 1\right) \cdot \left(1 - m\right) \]

  3. Final simplification0.1

    \[\leadsto \left(\frac{m - {m}^{2}}{v} - 1\right) \cdot \left(1 - m\right) \]

Reproduce

herbie shell --seed 2021224 
(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)))