a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.5%

Time: 6.7s

Alternatives: 9

Speedup: 1.0×

• 41.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 3.5 \cdot 10^{-32}:\\ \;\;\;\;m \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 3.5e-32) (* m (+ -1.0 (/ m v))) (/ m (/ v (* m (- 1.0 m))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 3.5e-32) {
		tmp = m * (-1.0 + (m / v));
	} else {
		tmp = m / (v / (m * (1.0 - m)));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 3.5d-32) then
        tmp = m * ((-1.0d0) + (m / v))
    else
        tmp = m / (v / (m * (1.0d0 - m)))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 3.5e-32) {
		tmp = m * (-1.0 + (m / v));
	} else {
		tmp = m / (v / (m * (1.0 - m)));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 3.5e-32:
		tmp = m * (-1.0 + (m / v))
	else:
		tmp = m / (v / (m * (1.0 - m)))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 3.5e-32)
		tmp = Float64(m * Float64(-1.0 + Float64(m / v)));
	else
		tmp = Float64(m / Float64(v / Float64(m * Float64(1.0 - m))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 3.5e-32)
		tmp = m * (-1.0 + (m / v));
	else
		tmp = m / (v / (m * (1.0 - m)));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 3.5e-32], N[(m * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(m / N[(v / N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 3.4999999999999999e-32

   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 99.8%

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

   if 3.4999999999999999e-32 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. flip-+ 21.9%

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

      2. associate-*r/ 21.1%

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

      3. metadata-eval 21.1%

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

      4. sub-neg 21.1%

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

      5. pow2 21.1%

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

      6. associate-/r/ 21.1%

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

      7. *-commutative 21.1%

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

      8. metadata-eval 21.1%

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

      9. div-inv 21.1%

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

      10. fma-neg 21.1%

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

      11. metadata-eval 21.1%

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

      12. clear-num 21.1%

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

   5. Applied egg-rr 21.1%

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

      1. associate-/l* 21.8%

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

      2. +-commutative 21.8%

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

   7. Simplified 21.8%

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

   8. 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 3.5 \cdot 10^{-32}:\\ \;\;\;\;m \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}}\\ \end{array} \]

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 3: 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%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

   1. clear-num 99.8%

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

   2. associate-/r/ 99.8%

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

   3. clear-num 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-/l* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 5: 75.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2 \cdot 10^{-149}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{-m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2e-149) (- m) (if (<= m 1.0) (/ m (/ v m)) (* m (/ (- m) v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2e-149) {
		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 <= 2d-149) 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 <= 2e-149) {
		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 <= 2e-149:
		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 <= 2e-149)
		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 <= 2e-149)
		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, 2e-149], (-m), If[LessEqual[m, 1.0], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], N[(m * N[((-m) / v), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 1.99999999999999996e-149

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-/l* 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in m around 0 71.2%

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

      1. neg-mul-1 71.2%

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

   6. Simplified 71.2%

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

   if 1.99999999999999996e-149 < m < 1

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-/l* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. flip-+ 68.0%

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

      2. associate-*r/ 68.0%

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

      3. metadata-eval 68.0%

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

      4. sub-neg 68.0%

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

      5. pow2 68.0%

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

      6. associate-/r/ 68.0%

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

      7. *-commutative 68.0%

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

      8. metadata-eval 68.0%

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

      9. div-inv 67.9%

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

      10. fma-neg 67.9%

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

      11. metadata-eval 67.9%

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

      12. clear-num 67.9%

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

   5. Applied egg-rr 67.9%

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

      1. associate-/l* 67.8%

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

      2. +-commutative 67.8%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in v around 0 81.7%

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

      1. associate-/r* 81.7%

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

   10. Simplified 81.7%

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

   11. Taylor expanded in m around 0 76.9%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. flip-+ 18.2%

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

      2. associate-*r/ 17.4%

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

      3. metadata-eval 17.4%

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

      4. sub-neg 17.4%

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

      5. pow2 17.4%

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

      6. associate-/r/ 17.4%

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

      7. *-commutative 17.4%

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

      8. metadata-eval 17.4%

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

      9. div-inv 17.4%

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

      10. fma-neg 17.4%

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

      11. metadata-eval 17.4%

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

      12. clear-num 17.4%

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

   5. Applied egg-rr 17.4%

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

      1. associate-/l* 18.2%

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

      2. +-commutative 18.2%

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

   7. Simplified 18.2%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. associate-/r* 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in m around 0 0.1%

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

       1. frac-2neg 0.1%

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

       2. associate-/r/ 0.1%

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

       3. remove-double-neg 0.1%

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

       4. frac-2neg 0.1%

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

       5. neg-mul-1 0.1%

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

       6. *-commutative 0.1%

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

       7. associate-*l* 0.1%

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

       8. *-commutative 0.1%

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

       9. associate-*l* 0.1%

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

       10. add-sqr-sqrt 0.0%

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

       11. sqrt-unprod 76.0%

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

       12. sqr-neg 76.0%

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

       13. sqrt-prod 76.0%

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

       14. add-sqr-sqrt 76.0%

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

   13. Applied egg-rr 76.0%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2 \cdot 10^{-149}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{-m}{v}\\ \end{array} \]

Alternative 6: 38.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.3 \cdot 10^{-147} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (or (<= m 2.3e-147) (not (<= m 1.0))) (- m) (* m (/ m v))))

C

double code(double m, double v) {
	double tmp;
	if ((m <= 2.3e-147) || !(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 <= 2.3d-147) .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 <= 2.3e-147) || !(m <= 1.0)) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (m <= 2.3e-147) or not (m <= 1.0):
		tmp = -m
	else:
		tmp = m * (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if ((m <= 2.3e-147) || !(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 <= 2.3e-147) || ~((m <= 1.0)))
		tmp = -m;
	else
		tmp = m * (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[Or[LessEqual[m, 2.3e-147], 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 < 2.2999999999999999e-147 or 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around 0 31.7%

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

      1. neg-mul-1 31.7%

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

   6. Simplified 31.7%

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

   if 2.2999999999999999e-147 < m < 1

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-/l* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. flip-+ 68.0%

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

      2. associate-*r/ 68.0%

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

      3. metadata-eval 68.0%

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

      4. sub-neg 68.0%

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

      5. pow2 68.0%

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

      6. associate-/r/ 68.0%

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

      7. *-commutative 68.0%

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

      8. metadata-eval 68.0%

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

      9. div-inv 67.9%

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

      10. fma-neg 67.9%

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

      11. metadata-eval 67.9%

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

      12. clear-num 67.9%

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

   5. Applied egg-rr 67.9%

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

      1. associate-/l* 67.8%

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

      2. +-commutative 67.8%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in v around 0 81.7%

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

      1. associate-/r* 81.7%

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

   10. Simplified 81.7%

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

   11. Taylor expanded in m around 0 76.9%

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

       1. associate-/r/ 76.8%

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

   13. Applied egg-rr 76.8%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.3 \cdot 10^{-147} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]

Alternative 7: 38.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.8 \cdot 10^{-149} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (or (<= m 2.8e-149) (not (<= m 1.0))) (- m) (/ m (/ v m))))

C

double code(double m, double v) {
	double tmp;
	if ((m <= 2.8e-149) || !(m <= 1.0)) {
		tmp = -m;
	} else {
		tmp = m / (v / m);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if ((m <= 2.8d-149) .or. (.not. (m <= 1.0d0))) then
        tmp = -m
    else
        tmp = m / (v / m)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if ((m <= 2.8e-149) || !(m <= 1.0)) {
		tmp = -m;
	} else {
		tmp = m / (v / m);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (m <= 2.8e-149) or not (m <= 1.0):
		tmp = -m
	else:
		tmp = m / (v / m)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if ((m <= 2.8e-149) || !(m <= 1.0))
		tmp = Float64(-m);
	else
		tmp = Float64(m / Float64(v / m));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if ((m <= 2.8e-149) || ~((m <= 1.0)))
		tmp = -m;
	else
		tmp = m / (v / m);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[Or[LessEqual[m, 2.8e-149], N[Not[LessEqual[m, 1.0]], $MachinePrecision]], (-m), N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.7999999999999999e-149 or 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around 0 31.7%

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

      1. neg-mul-1 31.7%

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

   6. Simplified 31.7%

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

   if 2.7999999999999999e-149 < m < 1

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-/l* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. flip-+ 68.0%

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

      2. associate-*r/ 68.0%

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

      3. metadata-eval 68.0%

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

      4. sub-neg 68.0%

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

      5. pow2 68.0%

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

      6. associate-/r/ 68.0%

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

      7. *-commutative 68.0%

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

      8. metadata-eval 68.0%

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

      9. div-inv 67.9%

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

      10. fma-neg 67.9%

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

      11. metadata-eval 67.9%

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

      12. clear-num 67.9%

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

   5. Applied egg-rr 67.9%

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

      1. associate-/l* 67.8%

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

      2. +-commutative 67.8%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in v around 0 81.7%

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

      1. associate-/r* 81.7%

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

   10. Simplified 81.7%

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

   11. Taylor expanded in m around 0 76.9%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.8 \cdot 10^{-149} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \end{array} \]

Alternative 8: 87.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   2. Taylor expanded in m around 0 97.5%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. flip-+ 18.2%

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

      2. associate-*r/ 17.4%

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

      3. metadata-eval 17.4%

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

      4. sub-neg 17.4%

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

      5. pow2 17.4%

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

      6. associate-/r/ 17.4%

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

      7. *-commutative 17.4%

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

      8. metadata-eval 17.4%

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

      9. div-inv 17.4%

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

      10. fma-neg 17.4%

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

      11. metadata-eval 17.4%

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

      12. clear-num 17.4%

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

   5. Applied egg-rr 17.4%

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

      1. associate-/l* 18.2%

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

      2. +-commutative 18.2%

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

   7. Simplified 18.2%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. associate-/r* 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in m around 0 0.1%

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

       1. frac-2neg 0.1%

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

       2. associate-/r/ 0.1%

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

       3. remove-double-neg 0.1%

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

       4. frac-2neg 0.1%

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

       5. neg-mul-1 0.1%

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

       6. *-commutative 0.1%

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

       7. associate-*l* 0.1%

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

       8. *-commutative 0.1%

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

       9. associate-*l* 0.1%

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

       10. add-sqr-sqrt 0.0%

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

       11. sqrt-unprod 76.0%

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

       12. sqr-neg 76.0%

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

       13. sqrt-prod 76.0%

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

       14. add-sqr-sqrt 76.0%

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

   13. Applied egg-rr 76.0%

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

4. Final simplification 87.9%

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

Alternative 9: 27.0% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	return -m

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-/l* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in m around 0 27.6%

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

   1. neg-mul-1 27.6%

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

6. Simplified 27.6%

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

7. Final simplification 27.6%

   \[\leadsto -m \]

Reproduce

herbie shell --seed 2023338 
(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))