a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.5%

Time: 10.2s

Alternatives: 12

Speedup: N/A×

• 41.9% 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: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - m}{\frac{v}{m \cdot m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.5e-24) (- (/ m (/ v m)) m) (/ (- 1.0 m) (/ v (* m m)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.5e-24) {
		tmp = (m / (v / m)) - m;
	} else {
		tmp = (1.0 - m) / (v / (m * 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 <= 1.5d-24) then
        tmp = (m / (v / m)) - m
    else
        tmp = (1.0d0 - m) / (v / (m * m))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.5e-24) {
		tmp = (m / (v / m)) - m;
	} else {
		tmp = (1.0 - m) / (v / (m * m));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.5e-24:
		tmp = (m / (v / m)) - m
	else:
		tmp = (1.0 - m) / (v / (m * m))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.5e-24)
		tmp = Float64(Float64(m / Float64(v / m)) - m);
	else
		tmp = Float64(Float64(1.0 - m) / Float64(v / Float64(m * m)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.5e-24)
		tmp = (m / (v / m)) - m;
	else
		tmp = (1.0 - m) / (v / (m * m));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.5e-24], N[(N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision], N[(N[(1.0 - m), $MachinePrecision] / N[(v / N[(m * m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.49999999999999998e-24

   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 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* 99.8%

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

   6. Simplified 99.8%

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

   if 1.49999999999999998e-24 < 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* 99.8%

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

      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 99.9%

      \[\leadsto \color{blue}{\frac{{m}^{2} \cdot \left(1 - m\right)}{v}} \]
   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-/l* 99.9%

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

   6. Simplified 99.9%

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

      1. associate-/l* 99.9%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/l* 99.9%

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

   8. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - m}{\frac{v}{m \cdot m}}\\ \end{array} \]

Alternative 2: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.2 \cdot 10^{-179}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 5.1 \cdot 10^{-168}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{elif}\;m \leq 1.18 \cdot 10^{-145}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m \cdot m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{-m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.2e-179)
   (- m)
   (if (<= m 5.1e-168)
     (/ m (/ v m))
     (if (<= m 1.18e-145)
       (- m)
       (if (<= m 1.0) (/ (* m m) v) (* m (/ (- m) v)))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.2e-179) {
		tmp = -m;
	} else if (m <= 5.1e-168) {
		tmp = m / (v / m);
	} else if (m <= 1.18e-145) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = (m * 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 <= 1.2d-179) then
        tmp = -m
    else if (m <= 5.1d-168) then
        tmp = m / (v / m)
    else if (m <= 1.18d-145) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = (m * 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 <= 1.2e-179) {
		tmp = -m;
	} else if (m <= 5.1e-168) {
		tmp = m / (v / m);
	} else if (m <= 1.18e-145) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = (m * m) / v;
	} else {
		tmp = m * (-m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.2e-179:
		tmp = -m
	elif m <= 5.1e-168:
		tmp = m / (v / m)
	elif m <= 1.18e-145:
		tmp = -m
	elif m <= 1.0:
		tmp = (m * m) / v
	else:
		tmp = m * (-m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.2e-179)
		tmp = Float64(-m);
	elseif (m <= 5.1e-168)
		tmp = Float64(m / Float64(v / m));
	elseif (m <= 1.18e-145)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(Float64(m * 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 <= 1.2e-179)
		tmp = -m;
	elseif (m <= 5.1e-168)
		tmp = m / (v / m);
	elseif (m <= 1.18e-145)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = (m * m) / v;
	else
		tmp = m * (-m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.2e-179], (-m), If[LessEqual[m, 5.1e-168], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 1.18e-145], (-m), If[LessEqual[m, 1.0], N[(N[(m * m), $MachinePrecision] / v), $MachinePrecision], N[(m * N[((-m) / v), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if m < 1.2e-179 or 5.0999999999999996e-168 < m < 1.18000000000000006e-145

   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 81.4%

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

      1. neg-mul-1 81.4%

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

   6. Simplified 81.4%

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

   if 1.2e-179 < m < 5.0999999999999996e-168

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. sub-neg 99.4%

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

      3. associate-/l* 99.4%

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

      4. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in v around 0 3.8%

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

      1. associate-*l/ 3.8%

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

      2. unpow2 3.8%

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

      3. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

      1. associate-/l* 3.8%

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

      2. associate-*l/ 3.8%

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

      3. *-commutative 3.8%

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

      4. associate-/l* 3.8%

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

   8. Applied egg-rr 3.8%

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

   9. Taylor expanded in m around 0 3.8%

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

       1. unpow2 3.8%

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

       2. associate-/l* 99.7%

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

   11. Simplified 99.7%

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

   if 1.18000000000000006e-145 < m < 1

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-/l* 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in v around 0 79.4%

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

      1. associate-/l* 79.4%

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

      2. unpow2 79.4%

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

   6. Simplified 79.4%

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

   7. Taylor expanded in m around 0 76.9%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. 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 0 0.1%

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

      1. associate-/l* 0.1%

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

      2. frac-2neg 0.1%

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

      3. associate-/r/ 0.1%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 82.9%

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

      6. sqr-neg 82.9%

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

      7. sqrt-unprod 82.2%

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

      8. add-sqr-sqrt 82.2%

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

   9. Applied egg-rr 82.2%

      \[\leadsto \color{blue}{\frac{m}{v} \cdot \left(-m\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.2 \cdot 10^{-179}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 5.1 \cdot 10^{-168}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{elif}\;m \leq 1.18 \cdot 10^{-145}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m \cdot m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{-m}{v}\\ \end{array} \]

Alternative 3: 38.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.8 \cdot 10^{-183}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 2.05 \cdot 10^{-171} \lor \neg \left(m \leq 1.4 \cdot 10^{-145}\right) \land m \leq 1:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.8e-183)
   (- m)
   (if (or (<= m 2.05e-171) (and (not (<= m 1.4e-145)) (<= m 1.0)))
     (* m (/ m v))
     (- m))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.8e-183) {
		tmp = -m;
	} else if ((m <= 2.05e-171) || (!(m <= 1.4e-145) && (m <= 1.0))) {
		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 (m <= 2.8d-183) then
        tmp = -m
    else if ((m <= 2.05d-171) .or. (.not. (m <= 1.4d-145)) .and. (m <= 1.0d0)) 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 (m <= 2.8e-183) {
		tmp = -m;
	} else if ((m <= 2.05e-171) || (!(m <= 1.4e-145) && (m <= 1.0))) {
		tmp = m * (m / v);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.8e-183:
		tmp = -m
	elif (m <= 2.05e-171) or (not (m <= 1.4e-145) and (m <= 1.0)):
		tmp = m * (m / v)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.8e-183)
		tmp = Float64(-m);
	elseif ((m <= 2.05e-171) || (!(m <= 1.4e-145) && (m <= 1.0)))
		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 (m <= 2.8e-183)
		tmp = -m;
	elseif ((m <= 2.05e-171) || (~((m <= 1.4e-145)) && (m <= 1.0)))
		tmp = m * (m / v);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.8e-183], (-m), If[Or[LessEqual[m, 2.05e-171], And[N[Not[LessEqual[m, 1.4e-145]], $MachinePrecision], LessEqual[m, 1.0]]], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], (-m)]]

Derivation

1. Split input into 2 regimes

2. if m < 2.79999999999999985e-183 or 2.05e-171 < m < 1.4000000000000001e-145 or 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      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 32.4%

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

      1. neg-mul-1 32.4%

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

   6. Simplified 32.4%

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

   if 2.79999999999999985e-183 < m < 2.05e-171 or 1.4000000000000001e-145 < m < 1

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-/l* 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in v around 0 73.7%

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

      1. associate-/l* 73.7%

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

      2. unpow2 73.7%

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

   6. Simplified 73.7%

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

   7. Taylor expanded in m around 0 71.3%

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

      1. associate-*l/ 78.5%

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

   9. Applied egg-rr 78.5%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.8 \cdot 10^{-183}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 2.05 \cdot 10^{-171} \lor \neg \left(m \leq 1.4 \cdot 10^{-145}\right) \land m \leq 1:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 4: 38.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 6.6 \cdot 10^{-182}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1.38 \cdot 10^{-170} \lor \neg \left(m \leq 1.6 \cdot 10^{-141}\right) \land m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 6.6e-182)
   (- m)
   (if (or (<= m 1.38e-170) (and (not (<= m 1.6e-141)) (<= m 1.0)))
     (/ m (/ v m))
     (- m))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 6.6e-182) {
		tmp = -m;
	} else if ((m <= 1.38e-170) || (!(m <= 1.6e-141) && (m <= 1.0))) {
		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 (m <= 6.6d-182) then
        tmp = -m
    else if ((m <= 1.38d-170) .or. (.not. (m <= 1.6d-141)) .and. (m <= 1.0d0)) 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 (m <= 6.6e-182) {
		tmp = -m;
	} else if ((m <= 1.38e-170) || (!(m <= 1.6e-141) && (m <= 1.0))) {
		tmp = m / (v / m);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 6.6e-182:
		tmp = -m
	elif (m <= 1.38e-170) or (not (m <= 1.6e-141) and (m <= 1.0)):
		tmp = m / (v / m)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 6.6e-182)
		tmp = Float64(-m);
	elseif ((m <= 1.38e-170) || (!(m <= 1.6e-141) && (m <= 1.0)))
		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 (m <= 6.6e-182)
		tmp = -m;
	elseif ((m <= 1.38e-170) || (~((m <= 1.6e-141)) && (m <= 1.0)))
		tmp = m / (v / m);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 6.6e-182], (-m), If[Or[LessEqual[m, 1.38e-170], And[N[Not[LessEqual[m, 1.6e-141]], $MachinePrecision], LessEqual[m, 1.0]]], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], (-m)]]

Derivation

1. Split input into 2 regimes

2. if m < 6.59999999999999991e-182 or 1.37999999999999996e-170 < m < 1.6000000000000001e-141 or 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      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 32.4%

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

      1. neg-mul-1 32.4%

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

   6. Simplified 32.4%

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

   if 6.59999999999999991e-182 < m < 1.37999999999999996e-170 or 1.6000000000000001e-141 < m < 1

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-/l* 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in v around 0 73.7%

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

      1. associate-*l/ 73.7%

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

      2. unpow2 73.7%

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

      3. associate-/l* 81.0%

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

   6. Simplified 81.0%

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

      1. associate-/l* 73.7%

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

      2. associate-*l/ 73.7%

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

      3. *-commutative 73.7%

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

      4. associate-/l* 73.6%

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

   8. Applied egg-rr 73.6%

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

   9. Taylor expanded in m around 0 71.3%

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

       1. unpow2 71.3%

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

       2. associate-/l* 78.6%

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

   11. Simplified 78.6%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 6.6 \cdot 10^{-182}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1.38 \cdot 10^{-170} \lor \neg \left(m \leq 1.6 \cdot 10^{-141}\right) \land m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 5: 38.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.6 \cdot 10^{-179}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 8.8 \cdot 10^{-169}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{elif}\;m \leq 1.02 \cdot 10^{-143}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m \cdot m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.6e-179)
   (- m)
   (if (<= m 8.8e-169)
     (/ m (/ v m))
     (if (<= m 1.02e-143) (- m) (if (<= m 1.0) (/ (* m m) v) (- m))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.6e-179) {
		tmp = -m;
	} else if (m <= 8.8e-169) {
		tmp = m / (v / m);
	} else if (m <= 1.02e-143) {
		tmp = -m;
	} else if (m <= 1.0) {
		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 (m <= 1.6d-179) then
        tmp = -m
    else if (m <= 8.8d-169) then
        tmp = m / (v / m)
    else if (m <= 1.02d-143) then
        tmp = -m
    else if (m <= 1.0d0) 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 (m <= 1.6e-179) {
		tmp = -m;
	} else if (m <= 8.8e-169) {
		tmp = m / (v / m);
	} else if (m <= 1.02e-143) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = (m * m) / v;
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.6e-179:
		tmp = -m
	elif m <= 8.8e-169:
		tmp = m / (v / m)
	elif m <= 1.02e-143:
		tmp = -m
	elif m <= 1.0:
		tmp = (m * m) / v
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.6e-179)
		tmp = Float64(-m);
	elseif (m <= 8.8e-169)
		tmp = Float64(m / Float64(v / m));
	elseif (m <= 1.02e-143)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(Float64(m * m) / v);
	else
		tmp = Float64(-m);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.6e-179)
		tmp = -m;
	elseif (m <= 8.8e-169)
		tmp = m / (v / m);
	elseif (m <= 1.02e-143)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = (m * m) / v;
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.6e-179], (-m), If[LessEqual[m, 8.8e-169], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 1.02e-143], (-m), If[LessEqual[m, 1.0], N[(N[(m * m), $MachinePrecision] / v), $MachinePrecision], (-m)]]]]

Derivation

1. Split input into 3 regimes

2. if m < 1.6e-179 or 8.80000000000000029e-169 < m < 1.02e-143 or 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      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 32.4%

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

      1. neg-mul-1 32.4%

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

   6. Simplified 32.4%

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

   if 1.6e-179 < m < 8.80000000000000029e-169

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. sub-neg 99.4%

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

      3. associate-/l* 99.4%

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

      4. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in v around 0 3.8%

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

      1. associate-*l/ 3.8%

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

      2. unpow2 3.8%

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

      3. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

      1. associate-/l* 3.8%

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

      2. associate-*l/ 3.8%

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

      3. *-commutative 3.8%

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

      4. associate-/l* 3.8%

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

   8. Applied egg-rr 3.8%

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

   9. Taylor expanded in m around 0 3.8%

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

       1. unpow2 3.8%

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

       2. associate-/l* 99.7%

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

   11. Simplified 99.7%

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

   if 1.02e-143 < m < 1

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-/l* 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in v around 0 79.4%

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

      1. associate-/l* 79.4%

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

      2. unpow2 79.4%

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

   6. Simplified 79.4%

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

   7. Taylor expanded in m around 0 76.9%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.6 \cdot 10^{-179}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 8.8 \cdot 10^{-169}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{elif}\;m \leq 1.02 \cdot 10^{-143}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m \cdot m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 6: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{m}{\frac{v}{m}}\\ \mathbf{if}\;m \leq 6 \cdot 10^{-25}:\\ \;\;\;\;t_0 - m\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (let* ((t_0 (/ m (/ v m)))) (if (<= m 6e-25) (- t_0 m) (* (- 1.0 m) t_0))))

C

double code(double m, double v) {
	double t_0 = m / (v / m);
	double tmp;
	if (m <= 6e-25) {
		tmp = t_0 - m;
	} else {
		tmp = (1.0 - m) * t_0;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: t_0
    real(8) :: tmp
    t_0 = m / (v / m)
    if (m <= 6d-25) then
        tmp = t_0 - m
    else
        tmp = (1.0d0 - m) * t_0
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double t_0 = m / (v / m);
	double tmp;
	if (m <= 6e-25) {
		tmp = t_0 - m;
	} else {
		tmp = (1.0 - m) * t_0;
	}
	return tmp;
}

Python

def code(m, v):
	t_0 = m / (v / m)
	tmp = 0
	if m <= 6e-25:
		tmp = t_0 - m
	else:
		tmp = (1.0 - m) * t_0
	return tmp

Julia

function code(m, v)
	t_0 = Float64(m / Float64(v / m))
	tmp = 0.0
	if (m <= 6e-25)
		tmp = Float64(t_0 - m);
	else
		tmp = Float64(Float64(1.0 - m) * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	t_0 = m / (v / m);
	tmp = 0.0;
	if (m <= 6e-25)
		tmp = t_0 - m;
	else
		tmp = (1.0 - m) * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := Block[{t$95$0 = N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[m, 6e-25], N[(t$95$0 - m), $MachinePrecision], N[(N[(1.0 - m), $MachinePrecision] * t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if m < 5.9999999999999995e-25

   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 86.6%

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

      1. neg-mul-1 86.6%

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

      2. +-commutative 86.6%

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

      3. unsub-neg 86.6%

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

      4. unpow2 86.6%

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

      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 5.9999999999999995e-25 < 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* 99.8%

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

      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 99.9%

      \[\leadsto \color{blue}{\frac{{m}^{2} \cdot \left(1 - m\right)}{v}} \]
   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-/l* 99.9%

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

   6. Simplified 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 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 6 \cdot 10^{-25}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \frac{m}{\frac{v}{m}}\\ \end{array} \]

Alternative 7: 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%

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

   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. Final simplification 99.8%

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

Alternative 8: 97.8% accurate, 1.1× speedup

Math

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

FPCore

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

Python

def code(m, v):
	tmp = 0
	if m <= 1.0:
		tmp = (m / (v / m)) - m
	else:
		tmp = m * (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(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 * (-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 * 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 86.5%

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

      1. neg-mul-1 86.5%

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

      2. +-commutative 86.5%

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

      3. unsub-neg 86.5%

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

      4. unpow2 86.5%

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

      5. associate-/l* 98.6%

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

   6. Simplified 98.6%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. 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 97.7%

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

      1. associate-*r/ 97.7%

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

      2. neg-mul-1 97.7%

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

   9. Simplified 97.7%

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

       1. frac-2neg 97.7%

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

       2. remove-double-neg 97.7%

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

       3. associate-/r/ 97.7%

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

       4. associate-*l/ 97.6%

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

       5. *-commutative 97.6%

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

   11. Applied egg-rr 97.6%

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

4. Final simplification 98.1%

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

Alternative 9: 97.8% accurate, 1.1× speedup

Math

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

FPCore

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

Python

def code(m, v):
	tmp = 0
	if m <= 1.0:
		tmp = (m / (v / m)) - m
	else:
		tmp = (m * 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(Float64(m * 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) * (-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[(N[(m * m), $MachinePrecision] * 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 86.5%

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

      1. neg-mul-1 86.5%

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

      2. +-commutative 86.5%

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

      3. unsub-neg 86.5%

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

      4. unpow2 86.5%

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

      5. associate-/l* 98.6%

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

   6. Simplified 98.6%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. 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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in m around inf 97.7%

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

       1. neg-mul-1 97.7%

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

       2. distribute-neg-frac 97.7%

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

   11. Simplified 97.7%

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

4. Final simplification 98.2%

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

Alternative 10: 88.0% 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. 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. associate-*r/ 99.7%

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

      3. fma-neg 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in m around 0 98.6%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. 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 0 0.1%

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

      1. associate-/l* 0.1%

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

      2. frac-2neg 0.1%

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

      3. associate-/r/ 0.1%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 82.9%

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

      6. sqr-neg 82.9%

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

      7. sqrt-unprod 82.2%

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

      8. add-sqr-sqrt 82.2%

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

   9. Applied egg-rr 82.2%

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

4. Final simplification 90.7%

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

Alternative 11: 88.0% 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 86.5%

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

      1. neg-mul-1 86.5%

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

      2. +-commutative 86.5%

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

      3. unsub-neg 86.5%

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

      4. unpow2 86.5%

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

      5. associate-/l* 98.6%

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

   6. Simplified 98.6%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. 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 0 0.1%

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

      1. associate-/l* 0.1%

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

      2. frac-2neg 0.1%

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

      3. associate-/r/ 0.1%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 82.9%

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

      6. sqr-neg 82.9%

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

      7. sqrt-unprod 82.2%

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

      8. add-sqr-sqrt 82.2%

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

   9. Applied egg-rr 82.2%

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

4. Final simplification 90.8%

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

Alternative 12: 27.4% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	return -m

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-/l* 99.8%

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

   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 28.8%

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

   1. neg-mul-1 28.8%

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

6. Simplified 28.8%

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

7. Final simplification 28.8%

   \[\leadsto -m \]

Reproduce

herbie shell --seed 2023287 
(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))