a parameter of renormalized beta distribution

Percentage Accurate: 99.9% → 99.8%

Time: 7.2s

Alternatives: 5

Speedup: N/A×

• 41.4% 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: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

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. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-*l/ 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 3.5 \cdot 10^{-15}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} \cdot \left(1 - m\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 3.5e-15) (* m (+ (/ m v) -1.0)) (* m (* (/ m v) (- 1.0 m)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 3.5e-15) {
		tmp = m * ((m / v) + -1.0);
	} 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 <= 3.5d-15) then
        tmp = m * ((m / v) + (-1.0d0))
    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 <= 3.5e-15) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = m * ((m / v) * (1.0 - m));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 3.5e-15:
		tmp = m * ((m / v) + -1.0)
	else:
		tmp = m * ((m / v) * (1.0 - m))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 3.5e-15)
		tmp = Float64(m * Float64(Float64(m / v) + -1.0));
	else
		tmp = Float64(m * Float64(Float64(m / v) * Float64(1.0 - m)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 3.5e-15)
		tmp = m * ((m / v) + -1.0);
	else
		tmp = m * ((m / v) * (1.0 - m));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 3.5e-15], N[(m * N[(N[(m / v), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(m * N[(N[(m / v), $MachinePrecision] * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 3.5000000000000001e-15

   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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in m around 0 99.8%

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

   if 3.5000000000000001e-15 < 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/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in v around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.9%

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

   7. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. unpow2 99.9%

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

      3. associate-*r* 100.0%

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

      4. div-inv 99.9%

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

      5. associate-*l* 99.9%

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

      6. add-sqr-sqrt 99.8%

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

      7. sqrt-unprod 92.2%

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

      8. sqr-neg 92.2%

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

      9. sqrt-unprod 0.0%

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

      10. add-sqr-sqrt 0.1%

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

      11. associate-/r/ 0.1%

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

      12. clear-num 0.1%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-unprod 92.2%

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

      15. sqr-neg 92.2%

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

      16. sqrt-unprod 99.8%

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

      17. add-sqr-sqrt 100.0%

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

   9. Applied egg-rr 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 3.5 \cdot 10^{-15}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} \cdot \left(1 - m\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.4% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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. 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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in m around 0 97.7%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in m around 0 5.6%

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

      1. neg-mul-1 5.6%

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

   7. Simplified 5.6%

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

4. Final simplification 52.7%

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

Alternative 4: 38.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 4.1 \cdot 10^{-175}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= v 4.1e-175) (* m (/ m v)) (- m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 4.1e-175) {
		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 <= 4.1d-175) 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 <= 4.1e-175) {
		tmp = m * (m / v);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 4.1e-175:
		tmp = m * (m / v)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 4.1e-175)
		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 <= 4.1e-175)
		tmp = m * (m / v);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 4.1e-175], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], (-m)]

Derivation

1. Split input into 2 regimes

2. if v < 4.09999999999999998e-175

   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%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in m around 0 36.5%

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

      1. neg-mul-1 36.5%

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

      2. +-commutative 36.5%

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

      3. unsub-neg 36.5%

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

   7. Simplified 36.5%

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

   8. Taylor expanded in m around inf 27.1%

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

      1. unpow2 27.1%

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

      2. associate-*l/ 39.1%

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

   10. Applied egg-rr 39.1%

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

   if 4.09999999999999998e-175 < v

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 39.2%

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

      1. neg-mul-1 39.2%

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

   7. Simplified 39.2%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq 4.1 \cdot 10^{-175}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 27.4% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	return -m

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-*l/ 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in m around 0 28.0%

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

   1. neg-mul-1 28.0%

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

7. Simplified 28.0%

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

8. Final simplification 28.0%

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

Reproduce

herbie shell --seed 2024024 
(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))