Average Error: 0.2 → 0.2

Time: 30.8s

Precision: binary64

Cost: 704

\[0 < m \land 0 < v \land v < 0.25\]

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

↓

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

\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m

↓

m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)

(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))

↓

(FPCore (m v) :precision binary64 (* m (- (/ (* m (- 1.0 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 * (1.0 - m)) / v) - 1.0);
}

Error

The X axis uses an exponential scale — Bits error versus `m`

Try it out

In
Out

Enter valid numbers for all inputs

Alternative 1
Accuracy	0.2
Cost	832

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

Alternative 2
Accuracy	0.9
Cost	1216

\[m \cdot \left(\frac{\frac{m - {m}^{4}}{1 + \left(m + m \cdot m\right)}}{v} - 1\right)\]

Alternative 3
Accuracy	9.6
Cost	1472

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

Derivation

Initial program 0.2
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
Using strategy rm
Applied pow1_binary640.2
\[\leadsto \left(\color{blue}{{\left(\frac{m \cdot \left(1 - m\right)}{v}\right)}^{1}} - 1\right) \cdot m\]
Final simplification0.2
\[\leadsto m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\]

Reproduce

herbie shell --seed 2020322 
(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))