a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 98.8%

Time: 6.8s

Alternatives: 13

Speedup: 1.0×

• 41.0% 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: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.05 \cdot 10^{-61}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot m}{\frac{v}{1 - m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.05e-61) (- (/ m (/ v m)) m) (/ (* m m) (/ v (- 1.0 m)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.05e-61) {
		tmp = (m / (v / m)) - m;
	} 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 <= 2.05d-61) then
        tmp = (m / (v / m)) - m
    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 <= 2.05e-61) {
		tmp = (m / (v / m)) - m;
	} else {
		tmp = (m * m) / (v / (1.0 - m));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.05e-61:
		tmp = (m / (v / m)) - m
	else:
		tmp = (m * m) / (v / (1.0 - m))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.05e-61)
		tmp = Float64(Float64(m / Float64(v / m)) - m);
	else
		tmp = Float64(Float64(m * m) / Float64(v / Float64(1.0 - m)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.05e-61)
		tmp = (m / (v / m)) - m;
	else
		tmp = (m * m) / (v / (1.0 - m));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.05e-61], N[(N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision], N[(N[(m * m), $MachinePrecision] / N[(v / N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.04999999999999999e-61

   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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in m around 0 85.7%

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

      1. neg-mul-1 85.7%

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

      2. +-commutative 85.7%

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

      3. unsub-neg 85.7%

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

      4. unpow2 85.7%

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

      5. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   if 2.04999999999999999e-61 < 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* 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in v around 0 99.8%

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

      1. associate-/l* 99.9%

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

      2. unpow2 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.05 \cdot 10^{-61}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot m}{\frac{v}{1 - m}}\\ \end{array} \]

Alternative 2: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{1 - m}{\frac{v}{m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.1e-16) (- (/ m (/ v m)) m) (* m (/ (- 1.0 m) (/ v m)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.1e-16) {
		tmp = (m / (v / m)) - m;
	} 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 <= 2.1d-16) then
        tmp = (m / (v / m)) - m
    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 <= 2.1e-16) {
		tmp = (m / (v / m)) - m;
	} else {
		tmp = m * ((1.0 - m) / (v / m));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.1e-16:
		tmp = (m / (v / m)) - m
	else:
		tmp = m * ((1.0 - m) / (v / m))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.1e-16)
		tmp = Float64(Float64(m / Float64(v / m)) - m);
	else
		tmp = Float64(m * Float64(Float64(1.0 - m) / Float64(v / m)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.1e-16)
		tmp = (m / (v / m)) - m;
	else
		tmp = m * ((1.0 - m) / (v / m));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.1e-16], N[(N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision], N[(m * N[(N[(1.0 - m), $MachinePrecision] / N[(v / m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.1000000000000001e-16

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-/l* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in m around 0 87.1%

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

      1. neg-mul-1 87.1%

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

      2. +-commutative 87.1%

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

      3. unsub-neg 87.1%

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

      4. unpow2 87.1%

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

      5. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

   if 2.1000000000000001e-16 < m

   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* 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. Taylor expanded in v around 0 99.9%

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

      1. associate-*l/ 99.9%

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

      2. unpow2 99.9%

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

      3. associate-*r/ 99.9%

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

      4. associate-*r* 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-*r/ 100.0%

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

      7. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{1 - m}{\frac{v}{m}}\\ \end{array} \]

Alternative 3: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.05 \cdot 10^{-61}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(m \cdot \frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.05e-61) (- (/ m (/ v m)) m) (* (- 1.0 m) (* m (/ m v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.05e-61) {
		tmp = (m / (v / m)) - m;
	} else {
		tmp = (1.0 - m) * (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 <= 2.05d-61) then
        tmp = (m / (v / m)) - m
    else
        tmp = (1.0d0 - m) * (m * (m / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 2.05e-61) {
		tmp = (m / (v / m)) - m;
	} else {
		tmp = (1.0 - m) * (m * (m / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.05e-61:
		tmp = (m / (v / m)) - m
	else:
		tmp = (1.0 - m) * (m * (m / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.05e-61)
		tmp = Float64(Float64(m / Float64(v / m)) - m);
	else
		tmp = Float64(Float64(1.0 - m) * Float64(m * Float64(m / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.05e-61)
		tmp = (m / (v / m)) - m;
	else
		tmp = (1.0 - m) * (m * (m / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.05e-61], N[(N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision], N[(N[(1.0 - m), $MachinePrecision] * N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.04999999999999999e-61

   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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in m around 0 85.7%

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

      1. neg-mul-1 85.7%

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

      2. +-commutative 85.7%

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

      3. unsub-neg 85.7%

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

      4. unpow2 85.7%

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

      5. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   if 2.04999999999999999e-61 < 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* 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in v around 0 99.8%

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

      1. associate-/l* 99.9%

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

      2. unpow2 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in v around 0 99.8%

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

      1. unpow2 99.8%

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

      2. associate-/l* 99.9%

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

      3. associate-/r/ 99.9%

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

      4. associate-*r/ 99.9%

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

   9. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.05 \cdot 10^{-61}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(m \cdot \frac{m}{v}\right)\\ \end{array} \]

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 5: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

   1. clear-num 99.8%

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

   2. associate-/r/ 99.8%

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

   3. clear-num 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 6: 74.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.48 \cdot 10^{-173}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{-m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.48e-173) (- m) (if (<= m 1.0) (/ m (/ v m)) (* m (/ (- m) v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.48e-173) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / 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 <= 1.48d-173) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = m / (v / 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 <= 1.48e-173) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = m * (-m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.48e-173:
		tmp = -m
	elif m <= 1.0:
		tmp = m / (v / m)
	else:
		tmp = m * (-m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.48e-173)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(m / Float64(v / m));
	else
		tmp = Float64(m * Float64(Float64(-m) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.48e-173)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = m / (v / m);
	else
		tmp = m * (-m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.48e-173], (-m), If[LessEqual[m, 1.0], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], N[(m * N[((-m) / v), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 1.48000000000000004e-173

   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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in m around 0 84.4%

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

      1. neg-mul-1 84.4%

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

   6. Simplified 84.4%

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

   if 1.48000000000000004e-173 < m < 1

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-/l* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in v around 0 65.1%

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

      1. associate-*l/ 65.2%

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

      2. unpow2 65.2%

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

      3. associate-*r/ 74.4%

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

      4. associate-*r* 74.4%

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

      5. *-commutative 74.4%

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

      6. associate-*r/ 74.4%

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

      7. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   7. Taylor expanded in m around 0 63.8%

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

      1. unpow2 63.8%

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

      2. associate-*r/ 73.0%

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

   9. Simplified 73.0%

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

   10. Taylor expanded in m around 0 63.8%

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

       1. unpow2 63.8%

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

       2. associate-/l* 73.0%

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

   12. Simplified 73.0%

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

   if 1 < m

   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* 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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in m around 0 0.1%

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

      1. associate-*l/ 0.1%

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

      2. *-un-lft-identity 0.1%

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

      3. frac-2neg 0.1%

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

      4. neg-sub0 0.1%

         \[\leadsto m \cdot \left(\frac{\color{blue}{0 - m}}{-v} + -1\right) \]

      5. metadata-eval 0.1%

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

      6. div-sub 0.1%

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

      7. metadata-eval 0.1%

         \[\leadsto m \cdot \left(\left(\frac{\color{blue}{0}}{-v} - \frac{m}{-v}\right) + -1\right) \]

      8. add-sqr-sqrt 0.1%

         \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{\sqrt{m} \cdot \sqrt{m}}}{-v}\right) + -1\right) \]

      9. sqrt-prod 0.1%

         \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{\sqrt{m \cdot m}}}{-v}\right) + -1\right) \]

      10. sqr-neg 0.1%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\sqrt{\color{blue}{\left(-m\right) \cdot \left(-m\right)}}}{-v}\right) + -1\right) \]

      11. sqrt-unprod 0.0%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{\sqrt{-m} \cdot \sqrt{-m}}}{-v}\right) + -1\right) \]

      12. add-sqr-sqrt 79.1%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{-m}}{-v}\right) + -1\right) \]

      13. frac-2neg 79.1%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \color{blue}{\frac{m}{v}}\right) + -1\right) \]

   8. Applied egg-rr 79.1%

      \[\leadsto m \cdot \left(\color{blue}{\left(\frac{0}{-v} - \frac{m}{v}\right)} + -1\right) \]
   9. Step-by-step derivation

      1. div0 79.1%

         \[\leadsto m \cdot \left(\left(\color{blue}{0} - \frac{m}{v}\right) + -1\right) \]

      2. neg-sub0 79.1%

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

      3. distribute-neg-frac 79.1%

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

   10. Simplified 79.1%

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

   11. Taylor expanded in m around inf 79.1%

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

       1. mul-1-neg 79.1%

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

       2. unpow2 79.1%

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

       3. associate-*l/ 79.1%

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

       4. distribute-rgt-neg-in 79.1%

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

   13. Simplified 79.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.48 \cdot 10^{-173}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{-m}{v}\\ \end{array} \]

Alternative 7: 97.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-/l* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in m around 0 86.7%

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

      1. neg-mul-1 86.7%

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

      2. +-commutative 86.7%

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

      3. unsub-neg 86.7%

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

      4. unpow2 86.7%

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

      5. associate-/l* 99.1%

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

   6. Simplified 99.1%

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

   if 1 < m

   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* 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. Taylor expanded in v around 0 99.9%

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

      1. associate-/l* 99.9%

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

      2. unpow2 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in m around inf 97.9%

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

      1. associate-*r/ 97.9%

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

      2. neg-mul-1 97.9%

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

   9. Simplified 97.9%

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

4. Final simplification 98.5%

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

Alternative 8: 87.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(m, v):
	tmp = 0
	if m <= 1.0:
		tmp = m * (-1.0 + (m / v))
	else:
		tmp = m * (-m / v)
	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(Float64(-m) / v));
	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 * (-m / v);
	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[((-m) / v), $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. Taylor expanded in m around 0 99.0%

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

   if 1 < m

   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* 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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in m around 0 0.1%

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

      1. associate-*l/ 0.1%

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

      2. *-un-lft-identity 0.1%

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

      3. frac-2neg 0.1%

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

      4. neg-sub0 0.1%

         \[\leadsto m \cdot \left(\frac{\color{blue}{0 - m}}{-v} + -1\right) \]

      5. metadata-eval 0.1%

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

      6. div-sub 0.1%

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

      7. metadata-eval 0.1%

         \[\leadsto m \cdot \left(\left(\frac{\color{blue}{0}}{-v} - \frac{m}{-v}\right) + -1\right) \]

      8. add-sqr-sqrt 0.1%

         \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{\sqrt{m} \cdot \sqrt{m}}}{-v}\right) + -1\right) \]

      9. sqrt-prod 0.1%

         \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{\sqrt{m \cdot m}}}{-v}\right) + -1\right) \]

      10. sqr-neg 0.1%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\sqrt{\color{blue}{\left(-m\right) \cdot \left(-m\right)}}}{-v}\right) + -1\right) \]

      11. sqrt-unprod 0.0%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{\sqrt{-m} \cdot \sqrt{-m}}}{-v}\right) + -1\right) \]

      12. add-sqr-sqrt 79.1%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{-m}}{-v}\right) + -1\right) \]

      13. frac-2neg 79.1%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \color{blue}{\frac{m}{v}}\right) + -1\right) \]

   8. Applied egg-rr 79.1%

      \[\leadsto m \cdot \left(\color{blue}{\left(\frac{0}{-v} - \frac{m}{v}\right)} + -1\right) \]
   9. Step-by-step derivation

      1. div0 79.1%

         \[\leadsto m \cdot \left(\left(\color{blue}{0} - \frac{m}{v}\right) + -1\right) \]

      2. neg-sub0 79.1%

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

      3. distribute-neg-frac 79.1%

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

   10. Simplified 79.1%

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

   11. Taylor expanded in m around inf 79.1%

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

       1. mul-1-neg 79.1%

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

       2. unpow2 79.1%

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

       3. associate-*l/ 79.1%

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

       4. distribute-rgt-neg-in 79.1%

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

   13. Simplified 79.1%

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

4. Final simplification 89.2%

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

Alternative 9: 87.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-/l* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in m around 0 86.7%

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

      1. neg-mul-1 86.7%

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

      2. +-commutative 86.7%

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

      3. unsub-neg 86.7%

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

      4. unpow2 86.7%

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

      5. associate-/l* 99.1%

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

   6. Simplified 99.1%

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

   if 1 < m

   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* 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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in m around 0 0.1%

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

      1. associate-*l/ 0.1%

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

      2. *-un-lft-identity 0.1%

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

      3. frac-2neg 0.1%

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

      4. neg-sub0 0.1%

         \[\leadsto m \cdot \left(\frac{\color{blue}{0 - m}}{-v} + -1\right) \]

      5. metadata-eval 0.1%

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

      6. div-sub 0.1%

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

      7. metadata-eval 0.1%

         \[\leadsto m \cdot \left(\left(\frac{\color{blue}{0}}{-v} - \frac{m}{-v}\right) + -1\right) \]

      8. add-sqr-sqrt 0.1%

         \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{\sqrt{m} \cdot \sqrt{m}}}{-v}\right) + -1\right) \]

      9. sqrt-prod 0.1%

         \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{\sqrt{m \cdot m}}}{-v}\right) + -1\right) \]

      10. sqr-neg 0.1%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\sqrt{\color{blue}{\left(-m\right) \cdot \left(-m\right)}}}{-v}\right) + -1\right) \]

      11. sqrt-unprod 0.0%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{\sqrt{-m} \cdot \sqrt{-m}}}{-v}\right) + -1\right) \]

      12. add-sqr-sqrt 79.1%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{-m}}{-v}\right) + -1\right) \]

      13. frac-2neg 79.1%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \color{blue}{\frac{m}{v}}\right) + -1\right) \]

   8. Applied egg-rr 79.1%

      \[\leadsto m \cdot \left(\color{blue}{\left(\frac{0}{-v} - \frac{m}{v}\right)} + -1\right) \]
   9. Step-by-step derivation

      1. div0 79.1%

         \[\leadsto m \cdot \left(\left(\color{blue}{0} - \frac{m}{v}\right) + -1\right) \]

      2. neg-sub0 79.1%

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

      3. distribute-neg-frac 79.1%

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

   10. Simplified 79.1%

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

   11. Taylor expanded in m around inf 79.1%

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

       1. mul-1-neg 79.1%

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

       2. unpow2 79.1%

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

       3. associate-*l/ 79.1%

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

       4. distribute-rgt-neg-in 79.1%

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

   13. Simplified 79.1%

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

4. Final simplification 89.2%

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

Alternative 10: 87.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

code[m_, v_] := If[LessEqual[m, 1.0], N[(N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision] - m), $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 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-/l* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in m around 0 86.7%

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

      1. neg-mul-1 86.7%

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

      2. +-commutative 86.7%

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

      3. unsub-neg 86.7%

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

      4. unpow2 86.7%

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

      5. associate-/l* 99.1%

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

   6. Simplified 99.1%

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

   if 1 < m

   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* 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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in m around 0 0.1%

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

      1. associate-*l/ 0.1%

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

      2. *-un-lft-identity 0.1%

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

      3. frac-2neg 0.1%

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

      4. neg-sub0 0.1%

         \[\leadsto m \cdot \left(\frac{\color{blue}{0 - m}}{-v} + -1\right) \]

      5. metadata-eval 0.1%

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

      6. div-sub 0.1%

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

      7. metadata-eval 0.1%

         \[\leadsto m \cdot \left(\left(\frac{\color{blue}{0}}{-v} - \frac{m}{-v}\right) + -1\right) \]

      8. add-sqr-sqrt 0.1%

         \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{\sqrt{m} \cdot \sqrt{m}}}{-v}\right) + -1\right) \]

      9. sqrt-prod 0.1%

         \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{\sqrt{m \cdot m}}}{-v}\right) + -1\right) \]

      10. sqr-neg 0.1%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\sqrt{\color{blue}{\left(-m\right) \cdot \left(-m\right)}}}{-v}\right) + -1\right) \]

      11. sqrt-unprod 0.0%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{\sqrt{-m} \cdot \sqrt{-m}}}{-v}\right) + -1\right) \]

      12. add-sqr-sqrt 79.1%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \frac{\color{blue}{-m}}{-v}\right) + -1\right) \]

      13. frac-2neg 79.1%

          \[\leadsto m \cdot \left(\left(\frac{0}{-v} - \color{blue}{\frac{m}{v}}\right) + -1\right) \]

   8. Applied egg-rr 79.1%

      \[\leadsto m \cdot \left(\color{blue}{\left(\frac{0}{-v} - \frac{m}{v}\right)} + -1\right) \]
   9. Step-by-step derivation

      1. div0 79.1%

         \[\leadsto m \cdot \left(\left(\color{blue}{0} - \frac{m}{v}\right) + -1\right) \]

      2. neg-sub0 79.1%

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

      3. distribute-neg-frac 79.1%

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

   10. Simplified 79.1%

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

4. Final simplification 89.2%

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

Alternative 11: 37.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 10^{-187}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= v 1e-187) (* m (/ m v)) (- m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 1e-187) {
		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 <= 1d-187) 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 <= 1e-187) {
		tmp = m * (m / v);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 1e-187:
		tmp = m * (m / v)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 1e-187)
		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 <= 1e-187)
		tmp = m * (m / v);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 1e-187], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], (-m)]

Derivation

1. Split input into 2 regimes

2. if v < 1e-187

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-/l* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in v around 0 77.5%

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

      1. associate-*l/ 77.5%

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

      2. unpow2 77.5%

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

      3. associate-*r/ 90.2%

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

      4. associate-*r* 90.2%

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

      5. *-commutative 90.2%

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

      6. associate-*r/ 90.2%

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

      7. associate-/l* 90.2%

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

   6. Simplified 90.2%

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

   7. Taylor expanded in m around 0 27.0%

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

      1. unpow2 27.0%

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

      2. associate-*r/ 39.7%

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

   9. Simplified 39.7%

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

   if 1e-187 < 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* 99.9%

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

      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. Taylor expanded in m around 0 43.0%

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

      1. neg-mul-1 43.0%

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

   6. Simplified 43.0%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq 10^{-187}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 12: 37.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 6.8 \cdot 10^{-188}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= v 6.8e-188) (/ m (/ v m)) (- m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 6.8e-188) {
		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 <= 6.8d-188) 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 <= 6.8e-188) {
		tmp = m / (v / m);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 6.8e-188:
		tmp = m / (v / m)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 6.8e-188)
		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 <= 6.8e-188)
		tmp = m / (v / m);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 6.8e-188], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], (-m)]

Derivation

1. Split input into 2 regimes

2. if v < 6.80000000000000055e-188

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-/l* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in v around 0 77.5%

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

      1. associate-*l/ 77.5%

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

      2. unpow2 77.5%

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

      3. associate-*r/ 90.2%

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

      4. associate-*r* 90.2%

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

      5. *-commutative 90.2%

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

      6. associate-*r/ 90.2%

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

      7. associate-/l* 90.2%

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

   6. Simplified 90.2%

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

   7. Taylor expanded in m around 0 27.0%

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

      1. unpow2 27.0%

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

      2. associate-*r/ 39.7%

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

   9. Simplified 39.7%

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

   10. Taylor expanded in m around 0 27.0%

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

       1. unpow2 27.0%

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

       2. associate-/l* 39.7%

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

   12. Simplified 39.7%

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

   if 6.80000000000000055e-188 < 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* 99.9%

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

      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. Taylor expanded in m around 0 43.0%

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

      1. neg-mul-1 43.0%

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

   6. Simplified 43.0%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq 6.8 \cdot 10^{-188}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 13: 27.3% 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 99.9%

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

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in m around 0 29.9%

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

   1. neg-mul-1 29.9%

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

6. Simplified 29.9%

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

7. Final simplification 29.9%

   \[\leadsto -m \]

Reproduce

herbie shell --seed 2023272 
(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))