a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 7.6s

Precision: binary64

Cost: 704

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

Math

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

↓

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

FPCore

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

↓

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

Python

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

↓

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

Derivation

1. Initial program 0.2

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

2. Simplified 0.2

   \[\leadsto \color{blue}{m \cdot \frac{m - m \cdot m}{v} - m} \]
   Proof

   [Start] 0.2	\[ \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.2	\[ \color{blue}{m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-102 [<=] 0.2	\[ \color{blue}{\frac{m \cdot \left(1 - m\right)}{v} \cdot m - m \cdot 1} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.2	\[ \color{blue}{m \cdot \frac{m \cdot \left(1 - m\right)}{v}} - m \cdot 1 \]
   rational_best_oopsla_all_46_json_45_simplify-13 [=>] 0.2	\[ m \cdot \frac{\color{blue}{1 \cdot m - m \cdot m}}{v} - m \cdot 1 \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.2	\[ m \cdot \frac{\color{blue}{m \cdot 1} - m \cdot m}{v} - m \cdot 1 \]
   rational_best_oopsla_all_46_json_45_simplify-52 [=>] 0.2	\[ m \cdot \frac{\color{blue}{m} - m \cdot m}{v} - m \cdot 1 \]
   rational_best_oopsla_all_46_json_45_simplify-52 [=>] 0.2	\[ m \cdot \frac{m - m \cdot m}{v} - \color{blue}{m} \]

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	0.7
Cost	708

\[\begin{array}{l} \mathbf{if}\;m \leq 7.8 \cdot 10^{-32}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(1 - m\right)}{v} \cdot m\\ \end{array} \]

Alternative 2
Error	0.2
Cost	704

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

Alternative 3
Error	24.6
Cost	452

\[\begin{array}{l} \mathbf{if}\;m \leq 4.4 \cdot 10^{-168}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot m\\ \end{array} \]

Alternative 4
Error	10.2
Cost	448

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

Alternative 5
Error	10.2
Cost	448

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

Alternative 6
Error	36.5
Cost	128

\[-m \]

Reproduce

herbie shell --seed 2023090 
(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))