a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 7.8s

Alternatives: 14

Speedup: N/A×

• 41.8% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in v around 0 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 9.5 \cdot 10^{-150}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{-m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 9.5e-150) (- m) (if (<= m 1.0) (/ m (/ v m)) (/ m (/ v (- m))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 9.5e-150) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = 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 <= 9.5d-150) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = m / (v / m)
    else
        tmp = m / (v / -m)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 9.5e-150) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = m / (v / -m);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 9.5e-150:
		tmp = -m
	elif m <= 1.0:
		tmp = m / (v / m)
	else:
		tmp = m / (v / -m)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 9.5e-150)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(m / Float64(v / m));
	else
		tmp = Float64(m / Float64(v / Float64(-m)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 9.5e-150)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = m / (v / m);
	else
		tmp = m / (v / -m);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 9.5e-150], (-m), If[LessEqual[m, 1.0], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], N[(m / N[(v / (-m)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 9.50000000000000013e-150

   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* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 71.3%

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

      1. neg-mul-1 71.3%

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

   7. Simplified 71.3%

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

   if 9.50000000000000013e-150 < 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* 99.4%

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

      4. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in v around 0 71.3%

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

      1. associate-/l* 71.1%

         \[\leadsto \color{blue}{{m}^{2} \cdot \frac{1 - m}{v}} \]

   7. Simplified 71.1%

      \[\leadsto \color{blue}{{m}^{2} \cdot \frac{1 - m}{v}} \]

   8. Taylor expanded in m around 0 65.4%

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

      1. unpow2 65.4%

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

      2. associate-*l* 65.4%

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

      3. div-inv 65.5%

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

      4. clear-num 65.6%

         \[\leadsto m \cdot \color{blue}{\frac{1}{\frac{v}{m}}} \]

      5. div-inv 65.7%

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

   10. Applied egg-rr 65.7%

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

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

   6. Taylor expanded in v around 0 99.9%

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

   7. Taylor expanded in m around 0 0.1%

      \[\leadsto m \cdot \frac{\color{blue}{m}}{v} \]
   8. Step-by-step derivation

      1. clear-num 0.1%

         \[\leadsto m \cdot \color{blue}{\frac{1}{\frac{v}{m}}} \]

      2. *-un-lft-identity 0.1%

         \[\leadsto m \cdot \frac{1}{\frac{\color{blue}{1 \cdot v}}{m}} \]

      3. associate-*l/ 0.1%

         \[\leadsto m \cdot \frac{1}{\color{blue}{\frac{1}{m} \cdot v}} \]

      4. div-inv 0.1%

         \[\leadsto \color{blue}{\frac{m}{\frac{1}{m} \cdot v}} \]

      5. frac-2neg 0.1%

         \[\leadsto \color{blue}{\frac{-m}{-\frac{1}{m} \cdot v}} \]

      6. add-sqr-sqrt 0.0%

         \[\leadsto \frac{\color{blue}{\sqrt{-m} \cdot \sqrt{-m}}}{-\frac{1}{m} \cdot v} \]

      7. sqrt-unprod 74.4%

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

      8. sqr-neg 74.4%

         \[\leadsto \frac{\sqrt{\color{blue}{m \cdot m}}}{-\frac{1}{m} \cdot v} \]

      9. sqrt-unprod 74.4%

         \[\leadsto \frac{\color{blue}{\sqrt{m} \cdot \sqrt{m}}}{-\frac{1}{m} \cdot v} \]

      10. add-sqr-sqrt 74.4%

          \[\leadsto \frac{\color{blue}{m}}{-\frac{1}{m} \cdot v} \]

      11. associate-*l/ 74.4%

          \[\leadsto \frac{m}{-\color{blue}{\frac{1 \cdot v}{m}}} \]

      12. *-un-lft-identity 74.4%

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

   9. Applied egg-rr 74.4%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 9.5 \cdot 10^{-150}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{-m}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.15 \cdot 10^{-15}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m \cdot \left(1 - m\right)}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.15e-15) (* m (/ (- m v) v)) (* m (/ (* m (- 1.0 m)) v))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.15e-15) {
		tmp = m * ((m - v) / v);
	} else {
		tmp = m * ((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 <= 1.15d-15) then
        tmp = m * ((m - v) / v)
    else
        tmp = m * ((m * (1.0d0 - m)) / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.15e-15) {
		tmp = m * ((m - v) / v);
	} else {
		tmp = m * ((m * (1.0 - m)) / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.15e-15:
		tmp = m * ((m - v) / v)
	else:
		tmp = m * ((m * (1.0 - m)) / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.15e-15)
		tmp = Float64(m * Float64(Float64(m - v) / v));
	else
		tmp = Float64(m * Float64(Float64(m * Float64(1.0 - m)) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.15e-15)
		tmp = m * ((m - v) / v);
	else
		tmp = m * ((m * (1.0 - m)) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.15e-15], N[(m * N[(N[(m - v), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision], N[(m * N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.14999999999999995e-15

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0 99.7%

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

   4. Taylor expanded in v around 0 99.7%

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

      1. neg-mul-1 99.7%

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

      2. unsub-neg 99.7%

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

   6. Simplified 99.7%

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

   if 1.14999999999999995e-15 < 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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

   6. Taylor expanded in v around 0 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.15 \cdot 10^{-15}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m \cdot \left(1 - m\right)}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 5.6 \cdot 10^{-16}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{\frac{v}{1 - m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 5.6e-16) (* m (/ (- m v) v)) (* m (/ m (/ v (- 1.0 m))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 5.6e-16) {
		tmp = m * ((m - v) / v);
	} else {
		tmp = m * (m / (v / (1.0 - 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 <= 5.6d-16) then
        tmp = m * ((m - v) / v)
    else
        tmp = m * (m / (v / (1.0d0 - m)))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 5.6e-16) {
		tmp = m * ((m - v) / v);
	} else {
		tmp = m * (m / (v / (1.0 - m)));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 5.6e-16:
		tmp = m * ((m - v) / v)
	else:
		tmp = m * (m / (v / (1.0 - m)))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 5.6e-16)
		tmp = Float64(m * Float64(Float64(m - v) / v));
	else
		tmp = Float64(m * Float64(m / Float64(v / Float64(1.0 - m))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 5.6e-16)
		tmp = m * ((m - v) / v);
	else
		tmp = m * (m / (v / (1.0 - m)));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 5.6e-16], N[(m * N[(N[(m - v), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision], N[(m * N[(m / N[(v / N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 5.6000000000000003e-16

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0 99.7%

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

   4. Taylor expanded in v around 0 99.7%

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

      1. neg-mul-1 99.7%

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

      2. unsub-neg 99.7%

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

   6. Simplified 99.7%

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

   if 5.6000000000000003e-16 < 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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{{m}^{2} \cdot \frac{1 - m}{v}} \]

   7. Simplified 99.9%

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

      1. clear-num 99.8%

         \[\leadsto {m}^{2} \cdot \color{blue}{\frac{1}{\frac{v}{1 - m}}} \]

      2. un-div-inv 99.9%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{\frac{v}{1 - m}}} \]

   9. Applied egg-rr 99.9%

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

       1. unpow2 99.9%

          \[\leadsto \frac{\color{blue}{m \cdot m}}{\frac{v}{1 - m}} \]

       2. associate-/l* 99.9%

          \[\leadsto \color{blue}{m \cdot \frac{m}{\frac{v}{1 - m}}} \]

   11. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 5.6 \cdot 10^{-16}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{\frac{v}{1 - m}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 5 \cdot 10^{-22}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(\left(1 - m\right) \cdot \frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 5e-22) (* m (/ (- m v) v)) (* m (* (- 1.0 m) (/ m v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 5e-22) {
		tmp = m * ((m - v) / v);
	} 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 <= 5d-22) then
        tmp = m * ((m - v) / v)
    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 <= 5e-22) {
		tmp = m * ((m - v) / v);
	} else {
		tmp = m * ((1.0 - m) * (m / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 5e-22:
		tmp = m * ((m - v) / v)
	else:
		tmp = m * ((1.0 - m) * (m / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 5e-22)
		tmp = Float64(m * Float64(Float64(m - v) / v));
	else
		tmp = Float64(m * Float64(Float64(1.0 - m) * Float64(m / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 5e-22)
		tmp = m * ((m - v) / v);
	else
		tmp = m * ((1.0 - m) * (m / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 5e-22], N[(m * N[(N[(m - v), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision], N[(m * N[(N[(1.0 - m), $MachinePrecision] * N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 4.99999999999999954e-22

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0 99.7%

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

   4. Taylor expanded in v around 0 99.7%

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

      1. neg-mul-1 99.7%

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

      2. unsub-neg 99.7%

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

   6. Simplified 99.7%

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

   if 4.99999999999999954e-22 < 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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

   6. Taylor expanded in v around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.9%

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

   8. Simplified 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 5 \cdot 10^{-22}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(\left(1 - m\right) \cdot \frac{m}{v}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.0)
		tmp = Float64(m * Float64(Float64(m - v) / v));
	else
		tmp = Float64(Float64(-m) * Float64(m / 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) / v);
	else
		tmp = -m * (m / (v / m));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0 96.9%

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

   4. Taylor expanded in v around 0 96.9%

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

      1. neg-mul-1 96.9%

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

      2. unsub-neg 96.9%

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

   6. Simplified 96.9%

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

   if 1 < m

   1. Initial program 99.9%

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

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{{m}^{2} \cdot \frac{1 - m}{v}} \]

   7. Simplified 99.9%

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

      1. clear-num 99.9%

         \[\leadsto {m}^{2} \cdot \color{blue}{\frac{1}{\frac{v}{1 - m}}} \]

      2. un-div-inv 99.9%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{\frac{v}{1 - m}}} \]

   9. Applied egg-rr 99.9%

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

       1. unpow2 99.9%

          \[\leadsto \frac{\color{blue}{m \cdot m}}{\frac{v}{1 - m}} \]

       2. associate-/l* 99.9%

          \[\leadsto \color{blue}{m \cdot \frac{m}{\frac{v}{1 - m}}} \]

   11. Applied egg-rr 99.9%

       \[\leadsto \color{blue}{m \cdot \frac{m}{\frac{v}{1 - m}}} \]

   12. Taylor expanded in m around inf 99.5%

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

       1. associate-*r/ 99.5%

          \[\leadsto m \cdot \frac{m}{\color{blue}{\frac{-1 \cdot v}{m}}} \]

       2. neg-mul-1 99.5%

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

   14. Simplified 99.5%

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

4. Final simplification 98.3%

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

Alternative 7: 86.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0 96.9%

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

   4. Taylor expanded in v around 0 96.9%

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

      1. neg-mul-1 96.9%

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

      2. unsub-neg 96.9%

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

   6. Simplified 96.9%

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

   if 1 < m

   1. Initial program 99.9%

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

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

   6. Taylor expanded in v around 0 99.9%

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

   7. Taylor expanded in m around 0 0.1%

      \[\leadsto m \cdot \frac{\color{blue}{m}}{v} \]
   8. Step-by-step derivation

      1. clear-num 0.1%

         \[\leadsto m \cdot \color{blue}{\frac{1}{\frac{v}{m}}} \]

      2. *-un-lft-identity 0.1%

         \[\leadsto m \cdot \frac{1}{\frac{\color{blue}{1 \cdot v}}{m}} \]

      3. associate-*l/ 0.1%

         \[\leadsto m \cdot \frac{1}{\color{blue}{\frac{1}{m} \cdot v}} \]

      4. div-inv 0.1%

         \[\leadsto \color{blue}{\frac{m}{\frac{1}{m} \cdot v}} \]

      5. frac-2neg 0.1%

         \[\leadsto \color{blue}{\frac{-m}{-\frac{1}{m} \cdot v}} \]

      6. add-sqr-sqrt 0.0%

         \[\leadsto \frac{\color{blue}{\sqrt{-m} \cdot \sqrt{-m}}}{-\frac{1}{m} \cdot v} \]

      7. sqrt-unprod 74.4%

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

      8. sqr-neg 74.4%

         \[\leadsto \frac{\sqrt{\color{blue}{m \cdot m}}}{-\frac{1}{m} \cdot v} \]

      9. sqrt-unprod 74.4%

         \[\leadsto \frac{\color{blue}{\sqrt{m} \cdot \sqrt{m}}}{-\frac{1}{m} \cdot v} \]

      10. add-sqr-sqrt 74.4%

          \[\leadsto \frac{\color{blue}{m}}{-\frac{1}{m} \cdot v} \]

      11. associate-*l/ 74.4%

          \[\leadsto \frac{m}{-\color{blue}{\frac{1 \cdot v}{m}}} \]

      12. *-un-lft-identity 74.4%

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

   9. Applied egg-rr 74.4%

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

4. Final simplification 84.9%

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

Alternative 8: 86.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.0) {
		tmp = m * (-1.0 + (m / v));
	} else {
		tmp = 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 * ((-1.0d0) + (m / v))
    else
        tmp = 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 * (-1.0 + (m / v));
	} else {
		tmp = m / (v / -m);
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0 96.9%

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

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

   6. Taylor expanded in v around 0 99.9%

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

   7. Taylor expanded in m around 0 0.1%

      \[\leadsto m \cdot \frac{\color{blue}{m}}{v} \]
   8. Step-by-step derivation

      1. clear-num 0.1%

         \[\leadsto m \cdot \color{blue}{\frac{1}{\frac{v}{m}}} \]

      2. *-un-lft-identity 0.1%

         \[\leadsto m \cdot \frac{1}{\frac{\color{blue}{1 \cdot v}}{m}} \]

      3. associate-*l/ 0.1%

         \[\leadsto m \cdot \frac{1}{\color{blue}{\frac{1}{m} \cdot v}} \]

      4. div-inv 0.1%

         \[\leadsto \color{blue}{\frac{m}{\frac{1}{m} \cdot v}} \]

      5. frac-2neg 0.1%

         \[\leadsto \color{blue}{\frac{-m}{-\frac{1}{m} \cdot v}} \]

      6. add-sqr-sqrt 0.0%

         \[\leadsto \frac{\color{blue}{\sqrt{-m} \cdot \sqrt{-m}}}{-\frac{1}{m} \cdot v} \]

      7. sqrt-unprod 74.4%

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

      8. sqr-neg 74.4%

         \[\leadsto \frac{\sqrt{\color{blue}{m \cdot m}}}{-\frac{1}{m} \cdot v} \]

      9. sqrt-unprod 74.4%

         \[\leadsto \frac{\color{blue}{\sqrt{m} \cdot \sqrt{m}}}{-\frac{1}{m} \cdot v} \]

      10. add-sqr-sqrt 74.4%

          \[\leadsto \frac{\color{blue}{m}}{-\frac{1}{m} \cdot v} \]

      11. associate-*l/ 74.4%

          \[\leadsto \frac{m}{-\color{blue}{\frac{1 \cdot v}{m}}} \]

      12. *-un-lft-identity 74.4%

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

   9. Applied egg-rr 74.4%

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

4. Final simplification 84.9%

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

Alternative 9: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

   1. associate-*r/ 99.8%

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

   2. *-commutative 99.8%

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

   3. associate-*r/ 99.8%

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

   4. clear-num 99.8%

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

   5. un-div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 10: 99.8% accurate, 1.0× speedup

Math

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

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

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

   1. clear-num 99.8%

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

   2. un-div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 11: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 12: 37.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 1.9 \cdot 10^{-178}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= v 1.9e-178) (/ m (/ v m)) (- m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 1.9e-178) {
		tmp = m / (v / m);
	} else {
		tmp = -m;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (v <= 1.9d-178) then
        tmp = m / (v / m)
    else
        tmp = -m
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (v <= 1.9e-178) {
		tmp = m / (v / m);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 1.9e-178:
		tmp = m / (v / m)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 1.9e-178)
		tmp = Float64(m / Float64(v / m));
	else
		tmp = Float64(-m);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (v <= 1.9e-178)
		tmp = m / (v / m);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 1.9e-178], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], (-m)]

Derivation

1. Split input into 2 regimes

2. if v < 1.90000000000000007e-178

   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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 77.7%

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

      1. associate-/l* 77.7%

         \[\leadsto \color{blue}{{m}^{2} \cdot \frac{1 - m}{v}} \]

   7. Simplified 77.7%

      \[\leadsto \color{blue}{{m}^{2} \cdot \frac{1 - m}{v}} \]

   8. Taylor expanded in m around 0 22.6%

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

      1. unpow2 22.6%

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

      2. associate-*l* 33.9%

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

      3. div-inv 33.9%

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

      4. clear-num 33.9%

         \[\leadsto m \cdot \color{blue}{\frac{1}{\frac{v}{m}}} \]

      5. div-inv 34.0%

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

   10. Applied egg-rr 34.0%

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

   if 1.90000000000000007e-178 < v

   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* 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in m around 0 36.3%

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

      1. neg-mul-1 36.3%

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

   7. Simplified 36.3%

      \[\leadsto \color{blue}{-m} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 37.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 2.05 \cdot 10^{-178}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= v 2.05e-178) (* m (/ m v)) (- m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 2.05e-178) {
		tmp = m * (m / v);
	} else {
		tmp = -m;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (v <= 2.05d-178) then
        tmp = m * (m / v)
    else
        tmp = -m
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (v <= 2.05e-178) {
		tmp = m * (m / v);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 2.05e-178:
		tmp = m * (m / v)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 2.05e-178)
		tmp = Float64(m * Float64(m / v));
	else
		tmp = Float64(-m);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (v <= 2.05e-178)
		tmp = m * (m / v);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 2.05e-178], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], (-m)]

Derivation

1. Split input into 2 regimes

2. if v < 2.05e-178

   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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 99.8%

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

   6. Taylor expanded in v around 0 89.0%

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

   7. Taylor expanded in m around 0 33.9%

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

   if 2.05e-178 < v

   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* 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in m around 0 36.3%

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

      1. neg-mul-1 36.3%

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

   7. Simplified 36.3%

      \[\leadsto \color{blue}{-m} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 27.2% 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%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in m around 0 25.9%

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

   1. neg-mul-1 25.9%

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

7. Simplified 25.9%

   \[\leadsto \color{blue}{-m} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024099 
(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))