a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.7%

Time: 5.0s

Alternatives: 10

Speedup: 1.0×

• 41.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 3.4 \cdot 10^{-15}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 3.4e-15) (- (* m (/ m v)) m) (/ m (/ v (* m (- 1.0 m))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 3.4e-15) {
		tmp = (m * (m / v)) - m;
	} 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 <= 3.4d-15) then
        tmp = (m * (m / v)) - m
    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 <= 3.4e-15) {
		tmp = (m * (m / v)) - m;
	} else {
		tmp = m / (v / (m * (1.0 - m)));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 3.4e-15:
		tmp = (m * (m / v)) - m
	else:
		tmp = m / (v / (m * (1.0 - m)))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 3.4e-15)
		tmp = Float64(Float64(m * Float64(m / v)) - m);
	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 <= 3.4e-15)
		tmp = (m * (m / v)) - m;
	else
		tmp = m / (v / (m * (1.0 - m)));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 3.4e-15], N[(N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision] - m), $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 < 3.4e-15

   1. Initial program 99.7%

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

   2. Taylor expanded in m around 0 84.5%

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

      1. neg-mul-1 84.5%

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

      2. +-commutative 84.5%

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

      3. unsub-neg 84.5%

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

      4. unpow2 84.5%

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

      5. associate-*r/ 99.7%

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

   4. Simplified 99.7%

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

   if 3.4e-15 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around inf 26.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{{m}^{3}}{v} + \frac{{m}^{2}}{v}} \]
   3. Step-by-step derivation

      1. +-commutative 26.5%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{v} + -1 \cdot \frac{{m}^{3}}{v}} \]

      2. mul-1-neg 26.5%

         \[\leadsto \frac{{m}^{2}}{v} + \color{blue}{\left(-\frac{{m}^{3}}{v}\right)} \]

      3. *-rgt-identity 26.5%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{v} \cdot 1} + \left(-\frac{{m}^{3}}{v}\right) \]

      4. unpow2 26.5%

         \[\leadsto \frac{\color{blue}{m \cdot m}}{v} \cdot 1 + \left(-\frac{{m}^{3}}{v}\right) \]

      5. associate-*r/ 26.5%

         \[\leadsto \color{blue}{\left(m \cdot \frac{m}{v}\right)} \cdot 1 + \left(-\frac{{m}^{3}}{v}\right) \]

      6. unpow3 26.5%

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

      7. unpow2 26.5%

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

      8. associate-/l* 26.5%

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

      9. unpow2 26.5%

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

      10. *-rgt-identity 26.5%

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

      11. times-frac 26.5%

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

      12. associate-/l* 26.5%

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

      13. unpow2 26.5%

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

      14. /-rgt-identity 26.5%

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

      15. distribute-rgt-neg-out 26.5%

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

      16. unpow2 26.5%

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

      17. associate-*r/ 26.5%

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

      18. distribute-lft-in 99.9%

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

      19. sub-neg 99.9%

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

      20. associate-*r* 99.9%

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

   4. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in v around 0 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 3.4 \cdot 10^{-15}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}}\\ \end{array} \]

Alternative 2: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 5.5 \cdot 10^{-15}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{\frac{v}{1 - m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 5.5e-15) (- (* m (/ m v)) m) (* m (/ m (/ v (- 1.0 m))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 5.5e-15) {
		tmp = (m * (m / v)) - m;
	} else {
		tmp = m * (m / (v / (1.0 - m)));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 5.5d-15) then
        tmp = (m * (m / v)) - m
    else
        tmp = m * (m / (v / (1.0d0 - m)))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 5.5e-15) {
		tmp = (m * (m / v)) - m;
	} else {
		tmp = m * (m / (v / (1.0 - m)));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 5.5e-15:
		tmp = (m * (m / v)) - m
	else:
		tmp = m * (m / (v / (1.0 - m)))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 5.5e-15)
		tmp = Float64(Float64(m * Float64(m / v)) - m);
	else
		tmp = Float64(m * Float64(m / Float64(v / Float64(1.0 - m))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 5.5e-15)
		tmp = (m * (m / v)) - m;
	else
		tmp = m * (m / (v / (1.0 - m)));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 5.5e-15], N[(N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision], N[(m * N[(m / N[(v / N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 5.5000000000000002e-15

   1. Initial program 99.7%

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

   2. Taylor expanded in m around 0 84.5%

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

      1. neg-mul-1 84.5%

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

      2. +-commutative 84.5%

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

      3. unsub-neg 84.5%

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

      4. unpow2 84.5%

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

      5. associate-*r/ 99.7%

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

   4. Simplified 99.7%

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

   if 5.5000000000000002e-15 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around inf 26.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{{m}^{3}}{v} + \frac{{m}^{2}}{v}} \]
   3. Step-by-step derivation

      1. +-commutative 26.5%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{v} + -1 \cdot \frac{{m}^{3}}{v}} \]

      2. mul-1-neg 26.5%

         \[\leadsto \frac{{m}^{2}}{v} + \color{blue}{\left(-\frac{{m}^{3}}{v}\right)} \]

      3. *-rgt-identity 26.5%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{v} \cdot 1} + \left(-\frac{{m}^{3}}{v}\right) \]

      4. unpow2 26.5%

         \[\leadsto \frac{\color{blue}{m \cdot m}}{v} \cdot 1 + \left(-\frac{{m}^{3}}{v}\right) \]

      5. associate-*r/ 26.5%

         \[\leadsto \color{blue}{\left(m \cdot \frac{m}{v}\right)} \cdot 1 + \left(-\frac{{m}^{3}}{v}\right) \]

      6. unpow3 26.5%

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

      7. unpow2 26.5%

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

      8. associate-/l* 26.5%

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

      9. unpow2 26.5%

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

      10. *-rgt-identity 26.5%

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

      11. times-frac 26.5%

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

      12. associate-/l* 26.5%

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

      13. unpow2 26.5%

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

      14. /-rgt-identity 26.5%

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

      15. distribute-rgt-neg-out 26.5%

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

      16. unpow2 26.5%

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

      17. associate-*r/ 26.5%

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

      18. distribute-lft-in 99.9%

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

      19. sub-neg 99.9%

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

      20. associate-*r* 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 5.5 \cdot 10^{-15}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{\frac{v}{1 - m}}\\ \end{array} \]

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

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(Float64(m / 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[(N[(m / v), $MachinePrecision] * N[(1.0 - m), $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. associate-/l* 99.8%

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

   2. associate-/r/ 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 4: 72.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.6 \cdot 10^{-196}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(-\frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.6e-196) (- m) (if (<= m 1.0) (/ m (/ v m)) (* m (- (/ m v))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.6e-196) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = m * -(m / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 2.6d-196) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = m / (v / m)
    else
        tmp = m * -(m / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 2.6e-196) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = m * -(m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.6e-196:
		tmp = -m
	elif m <= 1.0:
		tmp = m / (v / m)
	else:
		tmp = m * -(m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.6e-196)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(m / Float64(v / m));
	else
		tmp = Float64(m * Float64(-Float64(m / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.6e-196)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = m / (v / m);
	else
		tmp = m * -(m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.6e-196], (-m), If[LessEqual[m, 1.0], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], N[(m * (-N[(m / v), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 2.5999999999999998e-196

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 82.4%

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

      1. neg-mul-1 82.4%

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

   4. Simplified 82.4%

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

   if 2.5999999999999998e-196 < m < 1

   1. Initial program 99.6%

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

   2. Taylor expanded in v around 0 59.8%

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

   3. Taylor expanded in m around 0 52.9%

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

      1. unpow2 52.9%

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

      2. associate-*r/ 63.5%

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

   5. Simplified 63.5%

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

      1. associate-*r/ 52.9%

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

      2. associate-/l* 63.6%

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

   7. Applied egg-rr 63.6%

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

   if 1 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in v around 0 100.0%

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

   3. Taylor expanded in m around 0 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*r/ 0.1%

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

   5. Simplified 0.1%

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

      1. associate-*r/ 0.1%

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

      2. associate-/l* 0.1%

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

   7. Applied egg-rr 0.1%

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

      1. div-inv 0.1%

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

      2. add-sqr-sqrt 0.1%

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

      3. sqrt-unprod 0.1%

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

      4. sqr-neg 0.1%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 81.2%

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

      7. associate-/r/ 81.2%

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

      8. associate-*l* 81.2%

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

      9. div-inv 81.2%

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

      10. *-commutative 81.2%

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

      11. distribute-frac-neg 81.2%

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

      12. distribute-rgt-neg-out 81.2%

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

   9. Applied egg-rr 81.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.6 \cdot 10^{-196}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(-\frac{m}{v}\right)\\ \end{array} \]

Alternative 5: 72.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.75 \cdot 10^{-196}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-m \cdot m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.75e-196) (- m) (if (<= m 1.0) (/ m (/ v m)) (/ (- (* m m)) v))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.75e-196) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = -(m * m) / v;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.75d-196) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = m / (v / m)
    else
        tmp = -(m * m) / v
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.75e-196) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = -(m * m) / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.75e-196:
		tmp = -m
	elif m <= 1.0:
		tmp = m / (v / m)
	else:
		tmp = -(m * m) / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.75e-196)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(m / Float64(v / m));
	else
		tmp = Float64(Float64(-Float64(m * m)) / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.75e-196)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = m / (v / m);
	else
		tmp = -(m * m) / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.75e-196], (-m), If[LessEqual[m, 1.0], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], N[((-N[(m * m), $MachinePrecision]) / v), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 1.75000000000000002e-196

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 82.4%

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

      1. neg-mul-1 82.4%

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

   4. Simplified 82.4%

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

   if 1.75000000000000002e-196 < m < 1

   1. Initial program 99.6%

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

   2. Taylor expanded in v around 0 59.8%

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

   3. Taylor expanded in m around 0 52.9%

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

      1. unpow2 52.9%

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

      2. associate-*r/ 63.5%

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

   5. Simplified 63.5%

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

      1. associate-*r/ 52.9%

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

      2. associate-/l* 63.6%

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

   7. Applied egg-rr 63.6%

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

   if 1 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in v around 0 100.0%

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

   3. Taylor expanded in m around 0 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*r/ 0.1%

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

   5. Simplified 0.1%

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

      1. frac-2neg 0.1%

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

      2. associate-*r/ 0.1%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 83.9%

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

      5. sqr-neg 83.9%

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

      6. sqrt-unprod 81.2%

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

      7. add-sqr-sqrt 81.2%

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

   7. Applied egg-rr 81.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.75 \cdot 10^{-196}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-m \cdot m}{v}\\ \end{array} \]

Alternative 6: 97.9% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Python

def code(m, v):
	tmp = 0
	if m <= 1.0:
		tmp = (m * (m / v)) - 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(m / v)) - 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 * (m / v)) - 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[(m / v), $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. Taylor expanded in m around 0 81.8%

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

      1. neg-mul-1 81.8%

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

      2. +-commutative 81.8%

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

      3. unsub-neg 81.8%

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

      4. unpow2 81.8%

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

      5. associate-*r/ 95.8%

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

   4. Simplified 95.8%

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

   if 1 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around inf 20.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{{m}^{3}}{v} + \frac{{m}^{2}}{v}} \]
   3. Step-by-step derivation

      1. +-commutative 20.9%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{v} + -1 \cdot \frac{{m}^{3}}{v}} \]

      2. mul-1-neg 20.9%

         \[\leadsto \frac{{m}^{2}}{v} + \color{blue}{\left(-\frac{{m}^{3}}{v}\right)} \]

      3. *-rgt-identity 20.9%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{v} \cdot 1} + \left(-\frac{{m}^{3}}{v}\right) \]

      4. unpow2 20.9%

         \[\leadsto \frac{\color{blue}{m \cdot m}}{v} \cdot 1 + \left(-\frac{{m}^{3}}{v}\right) \]

      5. associate-*r/ 20.9%

         \[\leadsto \color{blue}{\left(m \cdot \frac{m}{v}\right)} \cdot 1 + \left(-\frac{{m}^{3}}{v}\right) \]

      6. unpow3 20.8%

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

      7. unpow2 20.9%

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

      8. associate-/l* 20.9%

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

      9. unpow2 20.9%

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

      10. *-rgt-identity 20.9%

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

      11. times-frac 20.8%

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

      12. associate-/l* 20.8%

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

      13. unpow2 20.8%

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

      14. /-rgt-identity 20.8%

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

      15. distribute-rgt-neg-out 20.8%

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

      16. unpow2 20.8%

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

      17. associate-*r/ 20.9%

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

      18. distribute-lft-in 99.9%

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

      19. sub-neg 99.9%

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

      20. associate-*r* 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in m around inf 96.0%

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

      1. mul-1-neg 96.0%

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

      2. unpow2 96.0%

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

      3. distribute-frac-neg 96.0%

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

      4. distribute-rgt-neg-out 96.0%

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

      5. *-rgt-identity 96.0%

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

      6. associate-*r/ 96.0%

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

      7. associate-*l* 96.0%

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

      8. associate-*r/ 96.0%

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

      9. *-rgt-identity 96.0%

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

   7. Simplified 96.0%

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

4. Final simplification 95.9%

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

Alternative 7: 97.9% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

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

   2. Taylor expanded in m around 0 81.8%

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

      1. neg-mul-1 81.8%

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

      2. +-commutative 81.8%

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

      3. unsub-neg 81.8%

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

      4. unpow2 81.8%

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

      5. associate-*r/ 95.8%

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

   4. Simplified 95.8%

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

   if 1 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around inf 20.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{{m}^{3}}{v} + \frac{{m}^{2}}{v}} \]
   3. Step-by-step derivation

      1. +-commutative 20.9%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{v} + -1 \cdot \frac{{m}^{3}}{v}} \]

      2. mul-1-neg 20.9%

         \[\leadsto \frac{{m}^{2}}{v} + \color{blue}{\left(-\frac{{m}^{3}}{v}\right)} \]

      3. *-rgt-identity 20.9%

         \[\leadsto \color{blue}{\frac{{m}^{2}}{v} \cdot 1} + \left(-\frac{{m}^{3}}{v}\right) \]

      4. unpow2 20.9%

         \[\leadsto \frac{\color{blue}{m \cdot m}}{v} \cdot 1 + \left(-\frac{{m}^{3}}{v}\right) \]

      5. associate-*r/ 20.9%

         \[\leadsto \color{blue}{\left(m \cdot \frac{m}{v}\right)} \cdot 1 + \left(-\frac{{m}^{3}}{v}\right) \]

      6. unpow3 20.8%

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

      7. unpow2 20.9%

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

      8. associate-/l* 20.9%

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

      9. unpow2 20.9%

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

      10. *-rgt-identity 20.9%

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

      11. times-frac 20.8%

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

      12. associate-/l* 20.8%

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

      13. unpow2 20.8%

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

      14. /-rgt-identity 20.8%

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

      15. distribute-rgt-neg-out 20.8%

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

      16. unpow2 20.8%

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

      17. associate-*r/ 20.9%

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

      18. distribute-lft-in 99.9%

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

      19. sub-neg 99.9%

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

      20. associate-*r* 99.9%

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

   4. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in m around inf 96.1%

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

      1. neg-mul-1 96.1%

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

      2. distribute-neg-frac 96.1%

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

   9. Simplified 96.1%

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

4. Final simplification 95.9%

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

Alternative 8: 87.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	tmp = 0
	if m <= 1.0:
		tmp = (m * (m / v)) - 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(m / v)) - m);
	else
		tmp = Float64(Float64(-Float64(m * m)) / v);
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

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

   2. Taylor expanded in m around 0 81.8%

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

      1. neg-mul-1 81.8%

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

      2. +-commutative 81.8%

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

      3. unsub-neg 81.8%

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

      4. unpow2 81.8%

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

      5. associate-*r/ 95.8%

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

   4. Simplified 95.8%

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

   if 1 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in v around 0 100.0%

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

   3. Taylor expanded in m around 0 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*r/ 0.1%

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

   5. Simplified 0.1%

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

      1. frac-2neg 0.1%

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

      2. associate-*r/ 0.1%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 83.9%

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

      5. sqr-neg 83.9%

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

      6. sqrt-unprod 81.2%

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

      7. add-sqr-sqrt 81.2%

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

   7. Applied egg-rr 81.2%

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

4. Final simplification 88.5%

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

Alternative 9: 38.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 8 \cdot 10^{-153}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= v 8e-153) (* m (/ m v)) (- m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 8e-153) {
		tmp = m * (m / v);
	} else {
		tmp = -m;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (v <= 8d-153) then
        tmp = m * (m / v)
    else
        tmp = -m
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (v <= 8e-153) {
		tmp = m * (m / v);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 8e-153:
		tmp = m * (m / v)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 8e-153)
		tmp = Float64(m * Float64(m / v));
	else
		tmp = Float64(-m);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (v <= 8e-153)
		tmp = m * (m / v);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 8e-153], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], (-m)]

Derivation

1. Split input into 2 regimes

2. if v < 8.00000000000000031e-153

   1. Initial program 99.8%

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

   2. Taylor expanded in v around 0 78.8%

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

   3. Taylor expanded in m around 0 24.4%

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

      1. unpow2 24.4%

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

      2. associate-*r/ 34.2%

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

   5. Simplified 34.2%

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

   if 8.00000000000000031e-153 < v

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 46.8%

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

      1. neg-mul-1 46.8%

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

   4. Simplified 46.8%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq 8 \cdot 10^{-153}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 10: 28.4% 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. Taylor expanded in m around 0 28.4%

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

   1. neg-mul-1 28.4%

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

4. Simplified 28.4%

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

5. Final simplification 28.4%

   \[\leadsto -m \]

Reproduce

herbie shell --seed 2023187 
(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))