a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 8.3s

Alternatives: 12

Speedup: 1.0×

• 41.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-/l* 99.8%

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

   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%

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

Alternative 2: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 4.5 \cdot 10^{-16}:\\ \;\;\;\;m \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m \cdot \left(1 - m\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 4.5e-16) (* m (+ -1.0 (/ m v))) (* (/ m v) (* m (- 1.0 m)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 4.5e-16) {
		tmp = m * (-1.0 + (m / v));
	} else {
		tmp = (m / v) * (m * (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 <= 4.5d-16) then
        tmp = m * ((-1.0d0) + (m / v))
    else
        tmp = (m / v) * (m * (1.0d0 - m))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 4.5e-16) {
		tmp = m * (-1.0 + (m / v));
	} else {
		tmp = (m / v) * (m * (1.0 - m));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 4.5e-16:
		tmp = m * (-1.0 + (m / v))
	else:
		tmp = (m / v) * (m * (1.0 - m))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 4.5e-16)
		tmp = Float64(m * Float64(-1.0 + Float64(m / v)));
	else
		tmp = Float64(Float64(m / v) * Float64(m * Float64(1.0 - m)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 4.5e-16)
		tmp = m * (-1.0 + (m / v));
	else
		tmp = (m / v) * (m * (1.0 - m));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 4.5e-16], N[(m * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m / v), $MachinePrecision] * N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 4.5000000000000002e-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%

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

   if 4.5000000000000002e-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%

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

      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. *-commutative 99.9%

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

      2. unpow2 99.9%

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

      3. associate-*r* 99.9%

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

      4. associate-*l/ 100.0%

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

      5. associate-*r/ 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-*l* 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 4.5 \cdot 10^{-16}:\\ \;\;\;\;m \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m \cdot \left(1 - m\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 4.4 \cdot 10^{-16}:\\ \;\;\;\;m \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 4.4e-16) (* m (+ -1.0 (/ m v))) (/ m (/ v (* m (- 1.0 m))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 4.4e-16) {
		tmp = m * (-1.0 + (m / v));
	} else {
		tmp = m / (v / (m * (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 <= 4.4d-16) then
        tmp = m * ((-1.0d0) + (m / v))
    else
        tmp = m / (v / (m * (1.0d0 - m)))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 4.4e-16) {
		tmp = m * (-1.0 + (m / v));
	} else {
		tmp = m / (v / (m * (1.0 - m)));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 4.4e-16:
		tmp = m * (-1.0 + (m / v))
	else:
		tmp = m / (v / (m * (1.0 - m)))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 4.4e-16)
		tmp = Float64(m * Float64(-1.0 + Float64(m / v)));
	else
		tmp = Float64(m / Float64(v / Float64(m * Float64(1.0 - m))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 4.4e-16)
		tmp = m * (-1.0 + (m / v));
	else
		tmp = m / (v / (m * (1.0 - m)));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 4.4e-16], N[(m * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(m / N[(v / N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 4.40000000000000001e-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%

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

   if 4.40000000000000001e-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%

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

      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. *-commutative 99.9%

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

      2. unpow2 99.9%

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

      3. associate-*r* 99.9%

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

      4. associate-*l/ 100.0%

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

      5. associate-*r/ 100.0%

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

   7. Applied egg-rr 100.0%

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

      1. clear-num 99.9%

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

      2. div-inv 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

      6. associate-/l/ 99.9%

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

      7. *-commutative 99.9%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 4.4 \cdot 10^{-16}:\\ \;\;\;\;m \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.8× speedup

Math

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

FPCore

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

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.0d0) then
        tmp = m * ((-1.0d0) + (m / 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 <= 1.0) {
		tmp = m * (-1.0 + (m / v));
	} else {
		tmp = m * (-1.0 - (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 * (-1.0 - (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(-1.0 - Float64(m * Float64(m / v))));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0 98.8%

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

   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%

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

      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 inf 98.1%

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

      1. neg-mul-1 98.1%

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

      2. distribute-neg-frac2 98.1%

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

   7. Simplified 98.1%

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

4. Final simplification 98.5%

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

Alternative 5: 62.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

code[m_, v_] := If[LessEqual[m, 1.0], N[(m / N[(v / m), $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. 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* 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in v around 0 45.5%

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

      1. *-commutative 45.5%

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

      2. unpow2 45.5%

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

      3. associate-*r* 45.5%

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

      4. associate-*l/ 52.6%

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

      5. associate-*r/ 52.6%

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

   7. Applied egg-rr 52.6%

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

      1. clear-num 52.5%

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

      2. div-inv 52.5%

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

      3. *-commutative 52.5%

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

      4. clear-num 52.5%

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

      5. un-div-inv 52.7%

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

      6. associate-/l/ 52.7%

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

      7. *-commutative 52.7%

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

   9. Applied egg-rr 52.7%

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

   10. Taylor expanded in m around 0 51.7%

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

   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%

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

      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 0 100.0%

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

   6. Taylor expanded in m around 0 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*l/ 0.1%

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

   8. Applied egg-rr 0.1%

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

      1. clear-num 0.1%

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

      2. associate-*l/ 0.1%

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

      3. *-un-lft-identity 0.1%

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

      4. div-inv 0.1%

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

      5. frac-2neg 0.1%

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

      6. add-sqr-sqrt 0.0%

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

      7. sqrt-unprod 81.5%

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

      8. sqr-neg 81.5%

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

      9. sqrt-prod 81.5%

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

      10. add-sqr-sqrt 81.5%

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

      11. div-inv 81.5%

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

   10. Applied egg-rr 81.5%

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

4. Final simplification 65.3%

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

Alternative 6: 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 7: 36.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 6.2 \cdot 10^{-149}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= m 6.2e-149) (- m) (* m (/ m v))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 6.2e-149) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 6.2d-149) then
        tmp = -m
    else
        tmp = m * (m / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 6.2e-149) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 6.2e-149:
		tmp = -m
	else:
		tmp = m * (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 6.2e-149)
		tmp = Float64(-m);
	else
		tmp = Float64(m * Float64(m / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 6.2e-149)
		tmp = -m;
	else
		tmp = m * (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 6.2e-149], (-m), N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 6.19999999999999974e-149

   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 77.7%

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

      1. neg-mul-1 77.7%

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

   7. Simplified 77.7%

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

   if 6.19999999999999974e-149 < m

   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* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in v around 0 90.7%

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

   6. Taylor expanded in m around 0 29.4%

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

      1. unpow2 29.4%

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

      2. associate-*l/ 29.4%

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

   8. Applied egg-rr 29.4%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 6.2 \cdot 10^{-149}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.65 \cdot 10^{-149}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= m 2.65e-149) (- m) (/ m (/ v m))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.65e-149) {
		tmp = -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 <= 2.65d-149) then
        tmp = -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 <= 2.65e-149) {
		tmp = -m;
	} else {
		tmp = m / (v / m);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.65e-149:
		tmp = -m
	else:
		tmp = m / (v / m)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.65e-149)
		tmp = Float64(-m);
	else
		tmp = Float64(m / Float64(v / m));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.65e-149)
		tmp = -m;
	else
		tmp = m / (v / m);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.65e-149], (-m), N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.65000000000000006e-149

   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 77.7%

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

      1. neg-mul-1 77.7%

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

   7. Simplified 77.7%

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

   if 2.65000000000000006e-149 < m

   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* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in v around 0 90.7%

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

      1. *-commutative 90.7%

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

      2. unpow2 90.7%

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

      3. associate-*r* 90.7%

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

      4. associate-*l/ 90.6%

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

      5. associate-*r/ 90.6%

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

   7. Applied egg-rr 90.6%

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

      1. clear-num 90.6%

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

      2. div-inv 90.6%

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

      3. *-commutative 90.6%

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

      4. clear-num 90.5%

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

      5. un-div-inv 90.6%

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

      6. associate-/l/ 90.6%

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

      7. *-commutative 90.6%

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

   9. Applied egg-rr 90.6%

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

   10. Taylor expanded in m around 0 29.4%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.65 \cdot 10^{-149}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := N[(m * N[(N[(1.0 - m), $MachinePrecision] * N[(m / v), $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. Taylor expanded in v around 0 70.4%

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

   1. *-commutative 70.4%

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

   2. unpow2 70.4%

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

   3. associate-*r* 70.4%

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

   4. associate-*l/ 74.3%

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

   5. associate-*r/ 74.3%

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

7. Applied egg-rr 74.3%

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

8. Final simplification 74.3%

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

Alternative 10: 63.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ m \cdot \frac{m + v}{-v} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := N[(m * N[(N[(m + 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. Add Preprocessing

3. Taylor expanded in m around 0 53.7%

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

4. Taylor expanded in v around 0 37.6%

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

   1. associate-*r* 37.6%

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

   2. neg-mul-1 37.6%

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

   3. unpow2 37.6%

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

   4. sqr-neg 37.6%

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

   5. distribute-lft-out 37.6%

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

   6. unsub-neg 37.6%

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

6. Simplified 37.6%

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

   1. frac-2neg 37.6%

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

   2. div-inv 37.5%

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

   3. distribute-lft-neg-out 37.5%

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

   4. remove-double-neg 37.5%

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

   5. sub-neg 37.5%

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

   6. +-commutative 37.5%

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

   7. add-sqr-sqrt 0.0%

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

   8. sqrt-unprod 51.5%

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

   9. sqr-neg 51.5%

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

   10. sqrt-prod 51.5%

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

   11. add-sqr-sqrt 51.5%

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

8. Applied egg-rr 51.5%

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

   1. associate-*l* 62.6%

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

   2. associate-*r/ 62.7%

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

   3. *-commutative 62.7%

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

   4. *-lft-identity 62.7%

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

10. Simplified 62.7%

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

11. Final simplification 62.7%

    \[\leadsto m \cdot \frac{m + v}{-v} \]
12. Add Preprocessing

Alternative 11: 48.8% accurate, 1.6× speedup

Math

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

FPCore

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

C

double code(double m, double v) {
	return 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 / v))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in m around 0 53.7%

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

4. Final simplification 53.7%

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

Alternative 12: 27.7% 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 28.2%

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

   1. neg-mul-1 28.2%

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

7. Simplified 28.2%

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

8. Final simplification 28.2%

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

Reproduce

herbie shell --seed 2024066 
(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))