b parameter of renormalized beta distribution

Average Error: 0.13% → 0.13%

Time: 6.6s

Precision: binary64

Cost: 832

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

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double m, double v) {
	return (1.0 - 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) * (1.0d0 - m)
end function

↓

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

↓

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

Python

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

↓

def code(m, v):
	return (1.0 - 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) * Float64(1.0 - m))
end

↓

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

↓

function tmp = code(m, v)
	tmp = (1.0 - 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] * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]

↓

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

Derivation

1. Initial program 0.13

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

2. Final simplification 0.13

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

Alternatives

Alternative 1
Error	0.34%
Cost	836

\[\begin{array}{l} \mathbf{if}\;m \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(\left(1 - m\right) \cdot \frac{m}{v}\right)\\ \end{array} \]

Alternative 2
Error	0.36%
Cost	836

\[\begin{array}{l} \mathbf{if}\;m \leq 1.5 \cdot 10^{-15}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \frac{m \cdot \left(1 - m\right)}{v}\\ \end{array} \]

Alternative 3
Error	0.13%
Cost	832

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

Alternative 4
Error	0.12%
Cost	832

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

Alternative 5
Error	3.67%
Cost	708

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

Alternative 6
Error	3.67%
Cost	708

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

Alternative 7
Error	3.67%
Cost	708

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

Alternative 8
Error	3.6%
Cost	708

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

Alternative 9
Error	3.6%
Cost	708

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

Alternative 10
Error	38.16%
Cost	589

\[\begin{array}{l} \mathbf{if}\;v \leq 1.35 \cdot 10^{-169} \lor \neg \left(v \leq 2.7 \cdot 10^{-146}\right) \land v \leq 1.05 \cdot 10^{-130}:\\ \;\;\;\;\frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m + -1\\ \end{array} \]

Alternative 11
Error	15.44%
Cost	448

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

Alternative 12
Error	58.39%
Cost	192

\[m + -1 \]

Alternative 13
Error	58.94%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023115 
(FPCore (m v)
  :name "b 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) (- 1.0 m)))