a parameter of renormalized beta distribution

Average Error: 99.7% → 99.7%

Time: 12.3s

Precision: binary64

Cost: 704.00

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

Math

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

↓

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

FPCore

(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)))

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 * (1.0 - m)) / v) + -1.0);
}

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 * (1.0d0 - m)) / v) + (-1.0d0))
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 * (1.0 - m)) / v) + -1.0);
}

Python

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

↓

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

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(m * Float64(Float64(Float64(m * Float64(1.0 - m)) / v) + -1.0))
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 * (1.0 - m)) / v) + -1.0);
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[(m * N[(N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7

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

2. Final simplification 99.7

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

Alternatives

Alternative 1
Error	62.4%
Cost	717.00

\[\begin{array}{l} \mathbf{if}\;v \leq 3.05 \cdot 10^{-130} \lor \neg \left(v \leq 4.4 \cdot 10^{-120}\right) \land v \leq 7.8 \cdot 10^{-115}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 2
Error	62.5%
Cost	717.00

\[\begin{array}{l} \mathbf{if}\;v \leq 3.7 \cdot 10^{-130} \lor \neg \left(v \leq 8.2 \cdot 10^{-121}\right) \land v \leq 1.3 \cdot 10^{-115}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 3
Error	62.5%
Cost	716.00

\[\begin{array}{l} \mathbf{if}\;v \leq 1.18 \cdot 10^{-129}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{elif}\;v \leq 7.8 \cdot 10^{-121}:\\ \;\;\;\;-m\\ \mathbf{elif}\;v \leq 1.15 \cdot 10^{-115}:\\ \;\;\;\;\frac{m \cdot m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 4
Error	99.2%
Cost	708.00

\[\begin{array}{l} \mathbf{if}\;m \leq 4.5 \cdot 10^{-9}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{\frac{v}{1 - m}}\\ \end{array} \]

Alternative 5
Error	99.2%
Cost	708.00

\[\begin{array}{l} \mathbf{if}\;m \leq 4.5 \cdot 10^{-9}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \frac{m \cdot m}{v}\\ \end{array} \]

Alternative 6
Error	99.7%
Cost	704.00

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

Alternative 7
Error	96.2%
Cost	644.00

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

Alternative 8
Error	96.2%
Cost	644.00

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

Alternative 9
Error	96.2%
Cost	644.00

\[\begin{array}{l} \mathbf{if}\;m \leq 1:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{-v}{m \cdot m}}\\ \end{array} \]

Alternative 10
Error	96.2%
Cost	644.00

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

Alternative 11
Error	84.2%
Cost	448.00

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

Alternative 12
Error	84.3%
Cost	448.00

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

Alternative 13
Error	42.9%
Cost	128.00

\[-m \]

Reproduce

herbie shell --seed 2023093 
(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))