a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 7.4s

Alternatives: 7

Speedup: 1.0×

• 41.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

\[\begin{array}{l} \\ \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \end{array} \]

FPCore

(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;
}

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

Java

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

Julia

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \end{array} \]

FPCore

(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;
}

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

Java

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

Julia

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
2. Step-by-step derivation

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-*l/ 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.6 \cdot 10^{-167}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(-1 - \frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.6e-167)
   (- m)
   (if (<= m 1.0) (* m (/ m v)) (* m (- -1.0 (/ m v))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.6e-167) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m * (m / v);
	} else {
		tmp = m * (-1.0 - (m / v));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.6d-167) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = m * (m / v)
    else
        tmp = m * ((-1.0d0) - (m / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.6e-167) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m * (m / v);
	} else {
		tmp = m * (-1.0 - (m / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.6e-167:
		tmp = -m
	elif m <= 1.0:
		tmp = m * (m / v)
	else:
		tmp = m * (-1.0 - (m / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.6e-167)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(m * Float64(m / v));
	else
		tmp = Float64(m * Float64(-1.0 - Float64(m / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.6e-167)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = m * (m / v);
	else
		tmp = m * (-1.0 - (m / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.6e-167], (-m), If[LessEqual[m, 1.0], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], N[(m * N[(-1.0 - N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 1.6000000000000001e-167

   1. Initial program 100.0%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in m around 0 84.4%

      \[\leadsto \color{blue}{-1 \cdot m} \]
   6. Step-by-step derivation

      1. neg-mul-1 84.4%

         \[\leadsto \color{blue}{-m} \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{-m} \]

   if 1.6000000000000001e-167 < m < 1

   1. Initial program 99.6%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l/ 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in m around 0 87.5%

      \[\leadsto \color{blue}{-1 \cdot m + \frac{{m}^{2}}{v}} \]
   6. Step-by-step derivation

      1. neg-mul-1 87.5%

         \[\leadsto \color{blue}{\left(-m\right)} + \frac{{m}^{2}}{v} \]

      2. +-commutative 87.5%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{v} + \left(-m\right)} \]

      3. unsub-neg 87.5%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - m} \]

   7. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - m} \]

   8. Taylor expanded in m around inf 66.2%

      \[\leadsto \color{blue}{\frac{{m}^{2}}{v}} \]
   9. Step-by-step derivation

      1. unpow2 66.2%

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

      2. associate-/l* 70.9%

         \[\leadsto \color{blue}{\frac{m}{\frac{v}{m}}} \]

      3. associate-/r/ 71.0%

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

   10. Applied egg-rr 71.0%

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

   if 1 < m

   1. Initial program 99.9%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. div-inv 99.9%

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

      3. associate-*l* 99.9%

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

      4. div-inv 99.9%

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

      5. metadata-eval 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in m around 0 0.1%

      \[\leadsto \left(m \cdot \color{blue}{\frac{1}{v}} + -1\right) \cdot m \]
   6. Step-by-step derivation

      1. fma-def 0.1%

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

      2. frac-2neg 0.1%

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

      3. metadata-eval 0.1%

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

      4. add-sqr-sqrt 0.0%

         \[\leadsto \mathsf{fma}\left(m, \frac{-1}{\color{blue}{\sqrt{-v} \cdot \sqrt{-v}}}, -1\right) \cdot m \]

      5. sqrt-unprod 88.3%

         \[\leadsto \mathsf{fma}\left(m, \frac{-1}{\color{blue}{\sqrt{\left(-v\right) \cdot \left(-v\right)}}}, -1\right) \cdot m \]

      6. sqr-neg 88.3%

         \[\leadsto \mathsf{fma}\left(m, \frac{-1}{\sqrt{\color{blue}{v \cdot v}}}, -1\right) \cdot m \]

      7. sqrt-unprod 86.0%

         \[\leadsto \mathsf{fma}\left(m, \frac{-1}{\color{blue}{\sqrt{v} \cdot \sqrt{v}}}, -1\right) \cdot m \]

      8. add-sqr-sqrt 86.0%

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

   7. Applied egg-rr 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(m, \frac{-1}{v}, -1\right)} \cdot m \]
   8. Step-by-step derivation

      1. fma-udef 86.0%

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

      2. associate-*r/ 86.0%

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

      3. *-commutative 86.0%

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

      4. mul-1-neg 86.0%

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

      5. distribute-neg-frac 86.0%

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

      6. +-commutative 86.0%

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

      7. sub-neg 86.0%

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

   9. Simplified 86.0%

      \[\leadsto \color{blue}{\left(-1 - \frac{m}{v}\right)} \cdot m \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.6 \cdot 10^{-167}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(-1 - \frac{m}{v}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.55 \cdot 10^{-167} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (or (<= m 1.55e-167) (not (<= m 1.0))) (- m) (* m (/ m v))))

C

double code(double m, double v) {
	double tmp;
	if ((m <= 1.55e-167) || !(m <= 1.0)) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if ((m <= 1.55d-167) .or. (.not. (m <= 1.0d0))) then
        tmp = -m
    else
        tmp = m * (m / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if ((m <= 1.55e-167) || !(m <= 1.0)) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (m <= 1.55e-167) or not (m <= 1.0):
		tmp = -m
	else:
		tmp = m * (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if ((m <= 1.55e-167) || !(m <= 1.0))
		tmp = Float64(-m);
	else
		tmp = Float64(m * Float64(m / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if ((m <= 1.55e-167) || ~((m <= 1.0)))
		tmp = -m;
	else
		tmp = m * (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[Or[LessEqual[m, 1.55e-167], N[Not[LessEqual[m, 1.0]], $MachinePrecision]], (-m), N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.55e-167 or 1 < m

   1. Initial program 99.9%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 33.7%

      \[\leadsto \color{blue}{-1 \cdot m} \]
   6. Step-by-step derivation

      1. neg-mul-1 33.7%

         \[\leadsto \color{blue}{-m} \]

   7. Simplified 33.7%

      \[\leadsto \color{blue}{-m} \]

   if 1.55e-167 < m < 1

   1. Initial program 99.6%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l/ 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in m around 0 87.5%

      \[\leadsto \color{blue}{-1 \cdot m + \frac{{m}^{2}}{v}} \]
   6. Step-by-step derivation

      1. neg-mul-1 87.5%

         \[\leadsto \color{blue}{\left(-m\right)} + \frac{{m}^{2}}{v} \]

      2. +-commutative 87.5%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{v} + \left(-m\right)} \]

      3. unsub-neg 87.5%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - m} \]

   7. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - m} \]

   8. Taylor expanded in m around inf 66.2%

      \[\leadsto \color{blue}{\frac{{m}^{2}}{v}} \]
   9. Step-by-step derivation

      1. unpow2 66.2%

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

      2. associate-/l* 70.9%

         \[\leadsto \color{blue}{\frac{m}{\frac{v}{m}}} \]

      3. associate-/r/ 71.0%

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

   10. Applied egg-rr 71.0%

       \[\leadsto \color{blue}{\frac{m}{v} \cdot m} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.55 \cdot 10^{-167} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.0) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = m * (-1.0 + (m / (-v / m)));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.0d0) then
        tmp = m * ((m / v) + (-1.0d0))
    else
        tmp = m * ((-1.0d0) + (m / (-v / m)))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.0) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = m * (-1.0 + (m / (-v / m)));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.0:
		tmp = m * ((m / v) + -1.0)
	else:
		tmp = m * (-1.0 + (m / (-v / m)))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.0)
		tmp = Float64(m * Float64(Float64(m / v) + -1.0));
	else
		tmp = Float64(m * Float64(-1.0 + Float64(m / Float64(Float64(-v) / m))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.0)
		tmp = m * ((m / v) + -1.0);
	else
		tmp = m * (-1.0 + (m / (-v / m)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. Add Preprocessing

   3. Taylor expanded in m around 0 95.9%

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

   if 1 < m

   1. Initial program 99.9%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around inf 97.9%

      \[\leadsto m \cdot \left(\frac{m}{\color{blue}{-1 \cdot \frac{v}{m}}} + -1\right) \]
   6. Step-by-step derivation

      1. associate-*r/ 97.9%

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

      2. neg-mul-1 97.9%

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

   7. Simplified 97.9%

      \[\leadsto m \cdot \left(\frac{m}{\color{blue}{\frac{-v}{m}}} + -1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.8%

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

Alternative 5: 98.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.0) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = m * (-1.0 - (m * (m / v)));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.0d0) then
        tmp = m * ((m / v) + (-1.0d0))
    else
        tmp = m * ((-1.0d0) - (m * (m / v)))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.0) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = m * (-1.0 - (m * (m / v)));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.0:
		tmp = m * ((m / v) + -1.0)
	else:
		tmp = m * (-1.0 - (m * (m / v)))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.0)
		tmp = Float64(m * Float64(Float64(m / v) + -1.0));
	else
		tmp = Float64(m * Float64(-1.0 - Float64(m * Float64(m / v))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.0)
		tmp = m * ((m / v) + -1.0);
	else
		tmp = m * (-1.0 - (m * (m / v)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. Add Preprocessing

   3. Taylor expanded in m around 0 95.9%

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

   if 1 < m

   1. Initial program 99.9%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. div-inv 99.9%

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

      3. associate-*l* 99.9%

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

      4. div-inv 99.9%

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

      5. metadata-eval 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in m around inf 97.9%

      \[\leadsto \left(m \cdot \color{blue}{\left(-1 \cdot \frac{m}{v}\right)} + -1\right) \cdot m \]
   6. Step-by-step derivation

      1. neg-mul-1 97.9%

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

      2. distribute-frac-neg 97.9%

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

   7. Simplified 97.9%

      \[\leadsto \left(m \cdot \color{blue}{\frac{-m}{v}} + -1\right) \cdot m \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

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

Alternative 6: 87.2% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.0) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = m * (-1.0 - (m / v));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.0d0) then
        tmp = m * ((m / v) + (-1.0d0))
    else
        tmp = m * ((-1.0d0) - (m / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.0) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = m * (-1.0 - (m / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.0:
		tmp = m * ((m / v) + -1.0)
	else:
		tmp = m * (-1.0 - (m / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.0)
		tmp = Float64(m * Float64(Float64(m / v) + -1.0));
	else
		tmp = Float64(m * Float64(-1.0 - Float64(m / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.0)
		tmp = m * ((m / v) + -1.0);
	else
		tmp = m * (-1.0 - (m / v));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. Add Preprocessing

   3. Taylor expanded in m around 0 95.9%

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

   if 1 < m

   1. Initial program 99.9%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. div-inv 99.9%

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

      3. associate-*l* 99.9%

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

      4. div-inv 99.9%

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

      5. metadata-eval 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in m around 0 0.1%

      \[\leadsto \left(m \cdot \color{blue}{\frac{1}{v}} + -1\right) \cdot m \]
   6. Step-by-step derivation

      1. fma-def 0.1%

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

      2. frac-2neg 0.1%

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

      3. metadata-eval 0.1%

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

      4. add-sqr-sqrt 0.0%

         \[\leadsto \mathsf{fma}\left(m, \frac{-1}{\color{blue}{\sqrt{-v} \cdot \sqrt{-v}}}, -1\right) \cdot m \]

      5. sqrt-unprod 88.3%

         \[\leadsto \mathsf{fma}\left(m, \frac{-1}{\color{blue}{\sqrt{\left(-v\right) \cdot \left(-v\right)}}}, -1\right) \cdot m \]

      6. sqr-neg 88.3%

         \[\leadsto \mathsf{fma}\left(m, \frac{-1}{\sqrt{\color{blue}{v \cdot v}}}, -1\right) \cdot m \]

      7. sqrt-unprod 86.0%

         \[\leadsto \mathsf{fma}\left(m, \frac{-1}{\color{blue}{\sqrt{v} \cdot \sqrt{v}}}, -1\right) \cdot m \]

      8. add-sqr-sqrt 86.0%

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

   7. Applied egg-rr 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(m, \frac{-1}{v}, -1\right)} \cdot m \]
   8. Step-by-step derivation

      1. fma-udef 86.0%

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

      2. associate-*r/ 86.0%

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

      3. *-commutative 86.0%

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

      4. mul-1-neg 86.0%

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

      5. distribute-neg-frac 86.0%

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

      6. +-commutative 86.0%

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

      7. sub-neg 86.0%

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

   9. Simplified 86.0%

      \[\leadsto \color{blue}{\left(-1 - \frac{m}{v}\right)} \cdot m \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.4%

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

Alternative 7: 27.6% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ -m \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (- m))

C

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

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    code = -m
end function

Java

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

Python

def code(m, v):
	return -m

Julia

function code(m, v)
	return Float64(-m)
end

MATLAB

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

Wolfram

code[m_, v_] := (-m)

Derivation

1. Initial program 99.8%

   \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
2. Step-by-step derivation

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-*l/ 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in m around 0 29.3%

   \[\leadsto \color{blue}{-1 \cdot m} \]
6. Step-by-step derivation

   1. neg-mul-1 29.3%

      \[\leadsto \color{blue}{-m} \]

7. Simplified 29.3%

   \[\leadsto \color{blue}{-m} \]

8. Final simplification 29.3%

   \[\leadsto -m \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024013 
(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))