a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 5.9s

Precision: binary64

Cost: 704

\[\left(0 < m \land 0 < v\right) \land v < 0.25\]

Math

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

↓

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

FPCore

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

↓

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

C

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))) - m;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    code = (((m * (1.0d0 - m)) / v) - 1.0d0) * m
end function

↓

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    code = (m * ((m / v) * (1.0d0 - m))) - m
end function

Java

public static double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * m;
}

↓

public static double code(double m, double v) {
	return (m * ((m / v) * (1.0 - m))) - m;
}

Python

def code(m, v):
	return (((m * (1.0 - m)) / v) - 1.0) * m

↓

def code(m, v):
	return (m * ((m / v) * (1.0 - m))) - m

Julia

function code(m, v)
	return Float64(Float64(Float64(Float64(m * Float64(1.0 - m)) / v) - 1.0) * m)
end

↓

function code(m, v)
	return Float64(Float64(m * Float64(Float64(m / v) * Float64(1.0 - m))) - m)
end

MATLAB

function tmp = code(m, v)
	tmp = (((m * (1.0 - m)) / v) - 1.0) * m;
end

↓

function tmp = code(m, v)
	tmp = (m * ((m / v) * (1.0 - m))) - m;
end

Wolfram

code[m_, v_] := N[(N[(N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision] - 1.0), $MachinePrecision] * m), $MachinePrecision]

↓

code[m_, v_] := N[(N[(m * N[(N[(m / v), $MachinePrecision] * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision]

Derivation

1. Initial program 0.2

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

2. Applied egg-rr 0.2

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

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	27.3
Cost	980

\[\begin{array}{l} t_0 := \frac{m}{\frac{v}{m}}\\ \mathbf{if}\;m \leq 1.6992919085069167 \cdot 10^{-238}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1.0047497444846973 \cdot 10^{-227}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;m \leq 2.7983102407303906 \cdot 10^{-188}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 5.449484237338686 \cdot 10^{-140}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;m \leq 5.925797845247041 \cdot 10^{-105}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	27.3
Cost	980

\[\begin{array}{l} t_0 := m \cdot \frac{m}{v}\\ \mathbf{if}\;m \leq 1.6992919085069167 \cdot 10^{-238}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1.0047497444846973 \cdot 10^{-227}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{elif}\;m \leq 2.7983102407303906 \cdot 10^{-188}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 5.449484237338686 \cdot 10^{-140}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;m \leq 5.925797845247041 \cdot 10^{-105}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	25.8
Cost	716

\[\begin{array}{l} t_0 := \frac{m \cdot m}{v}\\ \mathbf{if}\;m \leq 2.878290040905972 \cdot 10^{-153}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 5.449484237338686 \cdot 10^{-140}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;m \leq 5.925797845247041 \cdot 10^{-105}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.3
Cost	708

\[\begin{array}{l} \mathbf{if}\;m \leq 2.0911720687250524 \cdot 10^{-13}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(m \cdot \frac{1 - m}{v}\right)\\ \end{array} \]

Alternative 5
Error	0.3
Cost	708

\[\begin{array}{l} \mathbf{if}\;m \leq 2.0911720687250524 \cdot 10^{-13}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(m \cdot \left(1 - m\right)\right)}{v}\\ \end{array} \]

Alternative 6
Error	0.2
Cost	704

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

Alternative 7
Error	0.2
Cost	704

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

Alternative 8
Error	2.5
Cost	644

\[\begin{array}{l} \mathbf{if}\;m \leq 0.0026025359552939355:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(m \cdot \left(-m\right)\right)}{v}\\ \end{array} \]

Alternative 9
Error	10.1
Cost	448

\[m \cdot \frac{m}{v} - m \]

Alternative 10
Error	10.1
Cost	448

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

Alternative 11
Error	36.8
Cost	128

\[-m \]

Reproduce

herbie shell --seed 2022225 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (and (< 0.0 m) (< 0.0 v)) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))