a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 8.1s

Precision: binary64

Cost: 704

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

Math

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

↓

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

FPCore

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

↓

(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) 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 * (1.0 - m)) / v) - 1.0) * 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 * (1.0d0 - m)) / v) - 1.0d0) * 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 * (1.0 - m)) / v) - 1.0) * m;
}

Python

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

↓

def code(m, v):
	return (((m * (1.0 - m)) / v) - 1.0) * 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(Float64(Float64(m * Float64(1.0 - m)) / v) - 1.0) * 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 * (1.0 - m)) / v) - 1.0) * 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[(N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision] - 1.0), $MachinePrecision] * m), $MachinePrecision]

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Alternatives

Alternative 1
Error	25.9
Cost	980

\[\begin{array}{l} t_0 := \frac{m}{v} \cdot m\\ \mathbf{if}\;v \leq 7 \cdot 10^{-222}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;v \leq 1.25 \cdot 10^{-199}:\\ \;\;\;\;-m\\ \mathbf{elif}\;v \leq 6.8 \cdot 10^{-183}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;v \leq 4.2 \cdot 10^{-167}:\\ \;\;\;\;-m\\ \mathbf{elif}\;v \leq 1.7 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 2
Error	25.9
Cost	980

\[\begin{array}{l} t_0 := \frac{m}{\frac{v}{m}}\\ \mathbf{if}\;v \leq 6.8 \cdot 10^{-222}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;v \leq 1.5 \cdot 10^{-199}:\\ \;\;\;\;-m\\ \mathbf{elif}\;v \leq 7.4 \cdot 10^{-183}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;v \leq 2.75 \cdot 10^{-167}:\\ \;\;\;\;-m\\ \mathbf{elif}\;v \leq 1.6 \cdot 10^{-143}:\\ \;\;\;\;\frac{m}{v} \cdot m\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 3
Error	0.4
Cost	708

\[\begin{array}{l} \mathbf{if}\;m \leq 5.7 \cdot 10^{-12}:\\ \;\;\;\;\left(\frac{m}{v} - 1\right) \cdot m\\ \mathbf{else}:\\ \;\;\;\;\left(m \cdot \frac{1 - m}{v}\right) \cdot m\\ \end{array} \]

Alternative 4
Error	0.4
Cost	708

\[\begin{array}{l} \mathbf{if}\;m \leq 5.7 \cdot 10^{-12}:\\ \;\;\;\;\left(\frac{m}{v} - 1\right) \cdot m\\ \mathbf{else}:\\ \;\;\;\;\left(\left(1 - m\right) \cdot \frac{m}{v}\right) \cdot m\\ \end{array} \]

Alternative 5
Error	0.2
Cost	704

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

Alternative 6
Error	10.7
Cost	448

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

Alternative 7
Error	37.0
Cost	128

\[-m \]

Reproduce

herbie shell --seed 2023067 
(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))