a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.7%

Time: 9.5s

Alternatives: 16

Speedup: N/A×

• 41.2% 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: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.7 \cdot 10^{-14}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.7e-14) (* m (/ (- m v) v)) (/ m (/ v (* m (- 1.0 m))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.7e-14) {
		tmp = m * ((m - v) / 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 <= 2.7d-14) then
        tmp = m * ((m - v) / 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 <= 2.7e-14) {
		tmp = m * ((m - v) / v);
	} else {
		tmp = m / (v / (m * (1.0 - m)));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.7e-14:
		tmp = m * ((m - v) / v)
	else:
		tmp = m / (v / (m * (1.0 - m)))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.7e-14)
		tmp = Float64(m * Float64(Float64(m - v) / 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 <= 2.7e-14)
		tmp = m * ((m - v) / v);
	else
		tmp = m / (v / (m * (1.0 - m)));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.7e-14], N[(m * N[(N[(m - v), $MachinePrecision] / v), $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 < 2.6999999999999999e-14

   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 99.7%

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

   4. Taylor expanded in v around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. sub-neg 99.7%

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

   6. Simplified 99.7%

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

   if 2.6999999999999999e-14 < 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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 99.8%

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

   6. Taylor expanded in v around 0 99.8%

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

      1. associate-/l* 99.8%

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

   8. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. div-inv 99.8%

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

      3. clear-num 99.8%

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

      4. un-div-inv 99.8%

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

      5. associate-/l/ 99.9%

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

   10. 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.7 \cdot 10^{-14}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.25 \cdot 10^{-127}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\left(m \cdot m\right) \cdot \frac{1}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(-1 - \frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.25e-127)
   (- m)
   (if (<= m 1.0) (* (* m m) (/ 1.0 v)) (* m (- -1.0 (/ m v))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.25e-127) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = (m * m) * (1.0 / v);
	} else {
		tmp = m * (-1.0 - (m / v));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.25d-127) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = (m * m) * (1.0d0 / v)
    else
        tmp = m * ((-1.0d0) - (m / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.25e-127) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = (m * m) * (1.0 / v);
	} else {
		tmp = m * (-1.0 - (m / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.25e-127:
		tmp = -m
	elif m <= 1.0:
		tmp = (m * m) * (1.0 / v)
	else:
		tmp = m * (-1.0 - (m / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.25e-127)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(Float64(m * m) * Float64(1.0 / v));
	else
		tmp = Float64(m * Float64(-1.0 - Float64(m / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.25e-127)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = (m * m) * (1.0 / v);
	else
		tmp = m * (-1.0 - (m / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.25e-127], (-m), If[LessEqual[m, 1.0], N[(N[(m * m), $MachinePrecision] * N[(1.0 / v), $MachinePrecision]), $MachinePrecision], N[(m * N[(-1.0 - N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 1.2499999999999999e-127

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

   6. Taylor expanded in m around 0 78.3%

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

      1. neg-mul-1 78.3%

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

   8. Simplified 78.3%

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

   if 1.2499999999999999e-127 < 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* 99.5%

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

      4. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in v around 0 78.0%

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

      1. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

      1. unpow2 78.0%

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

   9. Applied egg-rr 78.0%

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

   10. Taylor expanded in m around 0 72.2%

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

   if 1 < 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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 99.8%

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

   6. Taylor expanded in m around 0 0.1%

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

      1. associate-*r/ 0.1%

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

      2. frac-2neg 0.1%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 0.1%

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

      5. mul-1-neg 0.1%

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

      6. mul-1-neg 0.1%

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

      7. sqr-neg 0.1%

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

      8. sqrt-unprod 0.1%

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

      9. add-sqr-sqrt 0.1%

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

      10. mul-1-neg 0.1%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 71.7%

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

      13. mul-1-neg 71.7%

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

      14. mul-1-neg 71.7%

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

      15. sqr-neg 71.7%

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

      16. sqrt-unprod 69.5%

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

      17. add-sqr-sqrt 69.5%

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

   8. Applied egg-rr 69.5%

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

      1. distribute-frac-neg 69.5%

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

      2. associate-/l* 69.5%

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

      3. distribute-lft-neg-in 69.5%

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

      4. *-lft-identity 69.5%

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

      5. associate-*l/ 69.5%

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

      6. distribute-rgt-in 69.5%

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

      7. rgt-mult-inverse 69.5%

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

      8. associate-*r/ 69.5%

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

      9. *-rgt-identity 69.5%

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

      10. distribute-lft-neg-out 69.5%

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

      11. distribute-rgt-neg-in 69.5%

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

      12. distribute-neg-in 69.5%

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

      13. metadata-eval 69.5%

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

      14. unsub-neg 69.5%

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

   10. Simplified 69.5%

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

Alternative 3: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 4.3 \cdot 10^{-142}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(-1 - \frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 4.3e-142)
   (- m)
   (if (<= m 1.0) (* m (/ m v)) (* m (- -1.0 (/ m v))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 4.3e-142) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m * (m / v);
	} else {
		tmp = m * (-1.0 - (m / v));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 4.3d-142) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = m * (m / v)
    else
        tmp = m * ((-1.0d0) - (m / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 4.3e-142) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m * (m / v);
	} else {
		tmp = m * (-1.0 - (m / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 4.3e-142:
		tmp = -m
	elif m <= 1.0:
		tmp = m * (m / v)
	else:
		tmp = m * (-1.0 - (m / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 4.3e-142)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(m * Float64(m / v));
	else
		tmp = Float64(m * Float64(-1.0 - Float64(m / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 4.3e-142)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = m * (m / v);
	else
		tmp = m * (-1.0 - (m / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 4.3e-142], (-m), If[LessEqual[m, 1.0], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], N[(m * N[(-1.0 - N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 4.2999999999999997e-142

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

   6. Taylor expanded in m around 0 79.7%

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

      1. neg-mul-1 79.7%

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

   8. Simplified 79.7%

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

   if 4.2999999999999997e-142 < 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* 99.5%

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

      4. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in v around 0 99.7%

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

   6. Taylor expanded in v around 0 75.9%

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

      1. associate-/l* 75.8%

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

   8. Simplified 75.8%

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

   9. Taylor expanded in m around 0 70.5%

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

   if 1 < 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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 99.8%

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

   6. Taylor expanded in m around 0 0.1%

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

      1. associate-*r/ 0.1%

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

      2. frac-2neg 0.1%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 0.1%

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

      5. mul-1-neg 0.1%

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

      6. mul-1-neg 0.1%

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

      7. sqr-neg 0.1%

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

      8. sqrt-unprod 0.1%

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

      9. add-sqr-sqrt 0.1%

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

      10. mul-1-neg 0.1%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 71.7%

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

      13. mul-1-neg 71.7%

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

      14. mul-1-neg 71.7%

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

      15. sqr-neg 71.7%

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

      16. sqrt-unprod 69.5%

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

      17. add-sqr-sqrt 69.5%

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

   8. Applied egg-rr 69.5%

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

      1. distribute-frac-neg 69.5%

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

      2. associate-/l* 69.5%

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

      3. distribute-lft-neg-in 69.5%

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

      4. *-lft-identity 69.5%

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

      5. associate-*l/ 69.5%

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

      6. distribute-rgt-in 69.5%

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

      7. rgt-mult-inverse 69.5%

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

      8. associate-*r/ 69.5%

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

      9. *-rgt-identity 69.5%

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

      10. distribute-lft-neg-out 69.5%

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

      11. distribute-rgt-neg-in 69.5%

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

      12. distribute-neg-in 69.5%

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

      13. metadata-eval 69.5%

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

      14. unsub-neg 69.5%

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

   10. Simplified 69.5%

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

Alternative 4: 38.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 8.5 \cdot 10^{-142} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (or (<= m 8.5e-142) (not (<= m 1.0))) (- m) (* m (/ m v))))

C

double code(double m, double v) {
	double tmp;
	if ((m <= 8.5e-142) || !(m <= 1.0)) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if ((m <= 8.5d-142) .or. (.not. (m <= 1.0d0))) then
        tmp = -m
    else
        tmp = m * (m / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if ((m <= 8.5e-142) || !(m <= 1.0)) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (m <= 8.5e-142) or not (m <= 1.0):
		tmp = -m
	else:
		tmp = m * (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if ((m <= 8.5e-142) || !(m <= 1.0))
		tmp = Float64(-m);
	else
		tmp = Float64(m * Float64(m / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if ((m <= 8.5e-142) || ~((m <= 1.0)))
		tmp = -m;
	else
		tmp = m * (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[Or[LessEqual[m, 8.5e-142], N[Not[LessEqual[m, 1.0]], $MachinePrecision]], (-m), N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 8.4999999999999996e-142 or 1 < 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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 99.8%

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

   6. Taylor expanded in m around 0 33.8%

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

      1. neg-mul-1 33.8%

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

   8. Simplified 33.8%

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

   if 8.4999999999999996e-142 < 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* 99.5%

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

      4. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in v around 0 99.7%

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

   6. Taylor expanded in v around 0 75.9%

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

      1. associate-/l* 75.8%

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

   8. Simplified 75.8%

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

   9. Taylor expanded in m around 0 70.5%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 8.5 \cdot 10^{-142} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 6.8 \cdot 10^{-15}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - m}{v} \cdot \left(m \cdot m\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 6.8e-15) (* m (/ (- m v) v)) (* (/ (- 1.0 m) v) (* m m))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 6.8e-15) {
		tmp = m * ((m - v) / v);
	} 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 <= 6.8d-15) then
        tmp = m * ((m - v) / v)
    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 <= 6.8e-15) {
		tmp = m * ((m - v) / v);
	} else {
		tmp = ((1.0 - m) / v) * (m * m);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 6.8e-15:
		tmp = m * ((m - v) / v)
	else:
		tmp = ((1.0 - m) / v) * (m * m)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 6.8e-15)
		tmp = Float64(m * Float64(Float64(m - v) / v));
	else
		tmp = Float64(Float64(Float64(1.0 - m) / v) * Float64(m * m));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 6.8e-15)
		tmp = m * ((m - v) / v);
	else
		tmp = ((1.0 - m) / v) * (m * m);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 6.8e-15], N[(m * N[(N[(m - v), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - m), $MachinePrecision] / v), $MachinePrecision] * N[(m * m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 6.8000000000000001e-15

   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 99.7%

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

   4. Taylor expanded in v around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. sub-neg 99.7%

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

   6. Simplified 99.7%

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

   if 6.8000000000000001e-15 < 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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 99.8%

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

      1. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

      1. unpow2 99.8%

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

   9. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 6.8 \cdot 10^{-15}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - m}{v} \cdot \left(m \cdot m\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 10^{-14}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m \cdot \left(1 - m\right)}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1e-14) (* m (/ (- m v) v)) (* m (/ (* m (- 1.0 m)) v))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1e-14) {
		tmp = m * ((m - v) / v);
	} else {
		tmp = m * ((m * (1.0 - m)) / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1d-14) then
        tmp = m * ((m - v) / v)
    else
        tmp = m * ((m * (1.0d0 - m)) / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1e-14) {
		tmp = m * ((m - v) / v);
	} else {
		tmp = m * ((m * (1.0 - m)) / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1e-14:
		tmp = m * ((m - v) / v)
	else:
		tmp = m * ((m * (1.0 - m)) / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1e-14)
		tmp = Float64(m * Float64(Float64(m - v) / v));
	else
		tmp = Float64(m * Float64(Float64(m * Float64(1.0 - m)) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1e-14)
		tmp = m * ((m - v) / v);
	else
		tmp = m * ((m * (1.0 - m)) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1e-14], N[(m * N[(N[(m - v), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision], N[(m * N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 9.99999999999999999e-15

   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 99.7%

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

   4. Taylor expanded in v around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. sub-neg 99.7%

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

   6. Simplified 99.7%

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

   if 9.99999999999999999e-15 < 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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 99.8%

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

   6. Taylor expanded in v around 0 99.8%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 10^{-14}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m \cdot \left(1 - m\right)}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.4 \cdot 10^{-13}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(m \cdot \frac{1 - m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.4e-13) (* m (/ (- m v) v)) (* m (* m (/ (- 1.0 m) v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.4e-13) {
		tmp = m * ((m - v) / v);
	} else {
		tmp = m * (m * ((1.0 - m) / v));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.4d-13) then
        tmp = m * ((m - v) / v)
    else
        tmp = m * (m * ((1.0d0 - m) / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.4e-13) {
		tmp = m * ((m - v) / v);
	} else {
		tmp = m * (m * ((1.0 - m) / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.4e-13:
		tmp = m * ((m - v) / v)
	else:
		tmp = m * (m * ((1.0 - m) / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.4e-13)
		tmp = Float64(m * Float64(Float64(m - v) / v));
	else
		tmp = Float64(m * Float64(m * Float64(Float64(1.0 - m) / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.4e-13)
		tmp = m * ((m - v) / v);
	else
		tmp = m * (m * ((1.0 - m) / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.4e-13], N[(m * N[(N[(m - v), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision], N[(m * N[(m * N[(N[(1.0 - m), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.4000000000000001e-13

   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 99.7%

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

   4. Taylor expanded in v around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. sub-neg 99.7%

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

   6. Simplified 99.7%

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

   if 1.4000000000000001e-13 < 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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 99.8%

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

   6. Taylor expanded in v around 0 99.8%

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

      1. associate-/l* 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.4 \cdot 10^{-13}:\\ \;\;\;\;m \cdot \frac{m - v}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(m \cdot \frac{1 - m}{v}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in m around 0 97.6%

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

   4. Taylor expanded in v around 0 97.6%

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

      1. mul-1-neg 97.6%

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

      2. sub-neg 97.6%

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

   6. Simplified 97.6%

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

   if 1 < 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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 99.8%

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

      1. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

      1. unpow2 99.8%

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

   9. Applied egg-rr 99.8%

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

   10. Taylor expanded in m around inf 97.8%

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

       1. neg-mul-1 97.8%

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

   12. Simplified 97.8%

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

4. Final simplification 97.7%

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

Alternative 9: 97.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in m around 0 97.6%

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

   4. Taylor expanded in v around 0 97.6%

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

      1. mul-1-neg 97.6%

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

      2. sub-neg 97.6%

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

   6. Simplified 97.6%

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

   if 1 < 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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 99.8%

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

   6. Taylor expanded in v around 0 99.8%

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

      1. associate-/l* 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in m around inf 97.7%

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

       1. neg-mul-1 97.8%

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

   11. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 10: 87.3% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in m around 0 97.6%

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

   4. Taylor expanded in v around 0 97.6%

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

      1. mul-1-neg 97.6%

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

      2. sub-neg 97.6%

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

   6. Simplified 97.6%

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

   if 1 < 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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 99.8%

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

   6. Taylor expanded in m around 0 0.1%

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

      1. associate-*r/ 0.1%

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

      2. frac-2neg 0.1%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 0.1%

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

      5. mul-1-neg 0.1%

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

      6. mul-1-neg 0.1%

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

      7. sqr-neg 0.1%

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

      8. sqrt-unprod 0.1%

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

      9. add-sqr-sqrt 0.1%

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

      10. mul-1-neg 0.1%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 71.7%

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

      13. mul-1-neg 71.7%

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

      14. mul-1-neg 71.7%

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

      15. sqr-neg 71.7%

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

      16. sqrt-unprod 69.5%

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

      17. add-sqr-sqrt 69.5%

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

   8. Applied egg-rr 69.5%

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

      1. distribute-frac-neg 69.5%

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

      2. associate-/l* 69.5%

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

      3. distribute-lft-neg-in 69.5%

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

      4. *-lft-identity 69.5%

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

      5. associate-*l/ 69.5%

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

      6. distribute-rgt-in 69.5%

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

      7. rgt-mult-inverse 69.5%

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

      8. associate-*r/ 69.5%

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

      9. *-rgt-identity 69.5%

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

      10. distribute-lft-neg-out 69.5%

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

      11. distribute-rgt-neg-in 69.5%

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

      12. distribute-neg-in 69.5%

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

      13. metadata-eval 69.5%

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

      14. unsub-neg 69.5%

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

   10. Simplified 69.5%

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

4. Final simplification 83.8%

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

Alternative 11: 87.3% accurate, 0.9× speedup

Math

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

FPCore

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in m around 0 97.6%

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

   if 1 < 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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in v around 0 99.8%

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

   6. Taylor expanded in m around 0 0.1%

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

      1. associate-*r/ 0.1%

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

      2. frac-2neg 0.1%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 0.1%

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

      5. mul-1-neg 0.1%

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

      6. mul-1-neg 0.1%

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

      7. sqr-neg 0.1%

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

      8. sqrt-unprod 0.1%

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

      9. add-sqr-sqrt 0.1%

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

      10. mul-1-neg 0.1%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 71.7%

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

      13. mul-1-neg 71.7%

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

      14. mul-1-neg 71.7%

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

      15. sqr-neg 71.7%

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

      16. sqrt-unprod 69.5%

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

      17. add-sqr-sqrt 69.5%

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

   8. Applied egg-rr 69.5%

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

      1. distribute-frac-neg 69.5%

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

      2. associate-/l* 69.5%

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

      3. distribute-lft-neg-in 69.5%

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

      4. *-lft-identity 69.5%

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

      5. associate-*l/ 69.5%

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

      6. distribute-rgt-in 69.5%

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

      7. rgt-mult-inverse 69.5%

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

      8. associate-*r/ 69.5%

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

      9. *-rgt-identity 69.5%

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

      10. distribute-lft-neg-out 69.5%

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

      11. distribute-rgt-neg-in 69.5%

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

      12. distribute-neg-in 69.5%

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

      13. metadata-eval 69.5%

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

      14. unsub-neg 69.5%

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

   10. Simplified 69.5%

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

4. Final simplification 83.8%

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

Alternative 12: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-/l* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in v around 0 99.8%

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

6. Final simplification 99.8%

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

Alternative 13: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-/l* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in m around 0 99.8%

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

   1. neg-mul-1 99.8%

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

   2. +-commutative 99.8%

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

   3. sub-neg 99.8%

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

   4. div-sub 99.8%

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

   5. associate-*r/ 99.8%

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

   6. associate-*l/ 99.8%

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

   7. associate-/r/ 99.8%

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

7. Simplified 99.8%

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

8. Final simplification 99.8%

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

Alternative 14: 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 15: 27.5% 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 v around 0 99.8%

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

6. Taylor expanded in m around 0 30.8%

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

   1. neg-mul-1 30.8%

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

8. Simplified 30.8%

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

Alternative 16: 3.1% accurate, 11.0× 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 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 30.8%

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

   1. *-commutative 30.8%

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

   2. neg-mul-1 30.8%

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

   3. neg-sub0 30.8%

      \[\leadsto \color{blue}{0 - m} \]

   4. sub-neg 30.8%

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

   5. add-sqr-sqrt 0.0%

      \[\leadsto 0 + \color{blue}{\sqrt{-m} \cdot \sqrt{-m}} \]

   6. sqrt-unprod 3.4%

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

   7. sqr-neg 3.4%

      \[\leadsto 0 + \sqrt{\color{blue}{m \cdot m}} \]

   8. sqrt-prod 3.2%

      \[\leadsto 0 + \color{blue}{\sqrt{m} \cdot \sqrt{m}} \]

   9. add-sqr-sqrt 3.2%

      \[\leadsto 0 + \color{blue}{m} \]

7. Applied egg-rr 3.2%

   \[\leadsto \color{blue}{0 + m} \]

8. Taylor expanded in m around 0 3.2%

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

Reproduce

herbie shell --seed 2024149 
(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))