Average Error: 0.2 → 0.2
Time: 8.8s
Precision: binary64
Cost: 704
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v) :precision binary64 (* m (- (/ m (/ v (- 1.0 m))) 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 / (1.0 - m))) - 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

Alternatives

Alternative 1
Error37.4
Cost27072
\[\left(\sqrt{m} \cdot \sqrt{\frac{m \cdot \left(1 - m\right)}{v} - 1}\right) \cdot \left(\sqrt{m} \cdot \sqrt{\frac{m \cdot \left(1 - m\right)}{v} - 1}\right)\]
Alternative 2
Error1.4
Cost21440
\[\sqrt[3]{m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)} \cdot \left(\sqrt[3]{m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)} \cdot \sqrt[3]{m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)}\right)\]
Alternative 3
Error0.8
Cost21184
\[\left(\sqrt[3]{\frac{m \cdot \left(1 - m\right)}{v} - 1} \cdot \sqrt[3]{\frac{m \cdot \left(1 - m\right)}{v} - 1}\right) \cdot \left(m \cdot \sqrt[3]{\frac{m \cdot \left(1 - m\right)}{v} - 1}\right)\]
Alternative 4
Error0.7
Cost20928
\[m \cdot \left(\sqrt[3]{\frac{m \cdot \left(1 - m\right)}{v}} \cdot \left(\sqrt[3]{\frac{m \cdot \left(1 - m\right)}{v}} \cdot \sqrt[3]{\frac{m \cdot \left(1 - m\right)}{v}}\right) - 1\right)\]
Alternative 5
Error0.9
Cost20160
\[m \cdot \left(\frac{m}{\sqrt[3]{v} \cdot \sqrt[3]{v}} \cdot \frac{1 - m}{\sqrt[3]{v}} - 1\right)\]
Alternative 6
Error1.4
Cost20160
\[\sqrt[3]{m} \cdot \left(\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(\sqrt[3]{m} \cdot \sqrt[3]{m}\right)\right)\]
Alternative 7
Error37.3
Cost14272
\[\sqrt{m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)} \cdot \sqrt{m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)}\]
Alternative 8
Error37.3
Cost14144
\[\sqrt{\frac{m \cdot \left(1 - m\right)}{v} - 1} \cdot \left(m \cdot \sqrt{\frac{m \cdot \left(1 - m\right)}{v} - 1}\right)\]
Alternative 9
Error9.6
Cost14016
\[m \cdot \left(\sqrt{\frac{m \cdot \left(1 - m\right)}{v}} \cdot \sqrt{\frac{m \cdot \left(1 - m\right)}{v}} - 1\right)\]
Alternative 10
Error0.4
Cost13632
\[m \cdot \left(\frac{m}{\sqrt{v}} \cdot \frac{1 - m}{\sqrt{v}} - 1\right)\]
Alternative 11
Error0.6
Cost13632
\[\sqrt{m} \cdot \left(\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \sqrt{m}\right)\]
Alternative 12
Error20.2
Cost13568
\[m \cdot \left(\sqrt[3]{{\left(\frac{m \cdot \left(1 - m\right)}{v}\right)}^{3}} - 1\right)\]
Alternative 13
Error42.6
Cost13568
\[\sqrt[3]{{\left(m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\right)}^{3}}\]
Alternative 14
Error11.5
Cost13504
\[m \cdot \left(e^{\log \left(\frac{m \cdot \left(1 - m\right)}{v}\right)} - 1\right)\]
Alternative 15
Error20.5
Cost8832
\[\frac{m \cdot \left({\left(\frac{m \cdot \left(1 - m\right)}{v}\right)}^{3} - 1\right)}{\left(1 + \frac{m \cdot \left(1 - m\right)}{v}\right) + \frac{m \cdot \left(1 - m\right)}{v} \cdot \frac{m \cdot \left(1 - m\right)}{v}}\]
Alternative 16
Error22.3
Cost8064
\[\frac{\frac{{m}^{3}}{v} \cdot \left(\left(1 - m\right) \cdot \frac{1 - m}{v}\right) - m}{1 + \frac{m \cdot \left(1 - m\right)}{v}}\]
Alternative 17
Error0.2
Cost7168
\[m \cdot \frac{m}{v} - \left(m + \frac{{m}^{3}}{v}\right)\]
Alternative 18
Error27.3
Cost7040
\[m \cdot \frac{m}{v} - \frac{{m}^{3}}{v}\]
Alternative 19
Error53.4
Cost6720
\[\frac{{\left(-m\right)}^{3}}{v}\]
Alternative 20
Error13.3
Cost1984
\[\frac{m \cdot \left(\left(\left(1 - m\right) \cdot \frac{m}{v}\right) \cdot \left(\left(1 - m\right) \cdot \frac{m}{v}\right) - 1\right)}{1 + \frac{\frac{m}{v}}{\frac{1}{1 - m}}}\]
Alternative 21
Error0.2
Cost1088
\[m \cdot \left(\frac{m \cdot \left(1 - m \cdot m\right)}{v \cdot \left(m + 1\right)} - 1\right)\]
Alternative 22
Error0.2
Cost1088
\[m \cdot \left(\frac{1 - m \cdot m}{v} \cdot \frac{m}{m + 1} - 1\right)\]
Alternative 23
Error0.2
Cost960
\[m \cdot \frac{m}{v} - \left(m + \frac{m}{v} \cdot \left(m \cdot m\right)\right)\]
Alternative 24
Error0.2
Cost832
\[m \cdot \left(\frac{\frac{m}{v}}{\frac{1}{1 - m}} - 1\right)\]
Alternative 25
Error0.2
Cost832
\[m \cdot \left(\frac{1}{\frac{v}{m \cdot \left(1 - m\right)}} - 1\right)\]
Alternative 26
Error0.2
Cost704
\[m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\]
Alternative 27
Error0.2
Cost704
\[m \cdot \left(m \cdot \frac{1 - m}{v} - 1\right)\]
Alternative 28
Error27.3
Cost576
\[m \cdot \frac{m}{\frac{v}{1 - m}}\]
Alternative 29
Error27.3
Cost576
\[\frac{m}{v} \cdot \left(m - m \cdot m\right)\]
Alternative 30
Error28.8
Cost576
\[m \cdot \left(-1 - m \cdot \frac{m}{v}\right)\]
Alternative 31
Error27.3
Cost576
\[m \cdot \frac{m \cdot \left(1 - m\right)}{v}\]
Alternative 32
Error10.6
Cost448
\[m \cdot \frac{m}{v} - m\]
Alternative 33
Error10.6
Cost448
\[m \cdot \left(\frac{m}{v} - 1\right)\]
Alternative 34
Error17.2
Cost448
\[\frac{m \cdot m}{v} - m\]
Alternative 35
Error36.4
Cost128
\[-m\]
Alternative 36
Error61.5
Cost64
\[1\]
Alternative 37
Error61.1
Cost64
\[0\]
Alternative 38
Error62.0
Cost64
\[-1\]

Error

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 associate-/l*_binary64_3640.2

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

  4. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2021022 
(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))