a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 8.7s

Alternatives: 10

Speedup: N/A×

• 41.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := N[(m * N[(N[(N[(1.0 - m), $MachinePrecision] / N[(v / 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* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

   1. *-commutative 99.8%

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

   2. div-inv 99.8%

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

   3. associate-*l* 99.8%

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

   4. associate-/r/ 99.8%

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

   5. un-div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := m \cdot \frac{m}{v}\\ \mathbf{if}\;m \leq 3.5 \cdot 10^{-186}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 5.6 \cdot 10^{-142}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;m \leq 4.2 \cdot 10^{-134}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(-1 - \frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (let* ((t_0 (* m (/ m v))))
   (if (<= m 3.5e-186)
     (- m)
     (if (<= m 5.6e-142)
       t_0
       (if (<= m 4.2e-134)
         (- m)
         (if (<= m 1.0) t_0 (* m (- -1.0 (/ m v)))))))))

C

double code(double m, double v) {
	double t_0 = m * (m / v);
	double tmp;
	if (m <= 3.5e-186) {
		tmp = -m;
	} else if (m <= 5.6e-142) {
		tmp = t_0;
	} else if (m <= 4.2e-134) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = t_0;
	} else {
		tmp = m * (-1.0 - (m / v));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: t_0
    real(8) :: tmp
    t_0 = m * (m / v)
    if (m <= 3.5d-186) then
        tmp = -m
    else if (m <= 5.6d-142) then
        tmp = t_0
    else if (m <= 4.2d-134) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = t_0
    else
        tmp = m * ((-1.0d0) - (m / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double t_0 = m * (m / v);
	double tmp;
	if (m <= 3.5e-186) {
		tmp = -m;
	} else if (m <= 5.6e-142) {
		tmp = t_0;
	} else if (m <= 4.2e-134) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = t_0;
	} else {
		tmp = m * (-1.0 - (m / v));
	}
	return tmp;
}

Python

def code(m, v):
	t_0 = m * (m / v)
	tmp = 0
	if m <= 3.5e-186:
		tmp = -m
	elif m <= 5.6e-142:
		tmp = t_0
	elif m <= 4.2e-134:
		tmp = -m
	elif m <= 1.0:
		tmp = t_0
	else:
		tmp = m * (-1.0 - (m / v))
	return tmp

Julia

function code(m, v)
	t_0 = Float64(m * Float64(m / v))
	tmp = 0.0
	if (m <= 3.5e-186)
		tmp = Float64(-m);
	elseif (m <= 5.6e-142)
		tmp = t_0;
	elseif (m <= 4.2e-134)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = t_0;
	else
		tmp = Float64(m * Float64(-1.0 - Float64(m / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	t_0 = m * (m / v);
	tmp = 0.0;
	if (m <= 3.5e-186)
		tmp = -m;
	elseif (m <= 5.6e-142)
		tmp = t_0;
	elseif (m <= 4.2e-134)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = t_0;
	else
		tmp = m * (-1.0 - (m / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := Block[{t$95$0 = N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[m, 3.5e-186], (-m), If[LessEqual[m, 5.6e-142], t$95$0, If[LessEqual[m, 4.2e-134], (-m), If[LessEqual[m, 1.0], t$95$0, N[(m * N[(-1.0 - N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if m < 3.49999999999999989e-186 or 5.60000000000000009e-142 < m < 4.1999999999999998e-134

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 82.0%

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

      1. neg-mul-1 82.0%

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

   7. Simplified 82.0%

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

   if 3.49999999999999989e-186 < m < 5.60000000000000009e-142 or 4.1999999999999998e-134 < m < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in m around 0 97.1%

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

   4. Taylor expanded in m around inf 64.3%

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

      1. unpow2 64.3%

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

      2. associate-*l/ 76.0%

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

   6. Applied egg-rr 76.0%

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

   if 1 < m

   1. Initial program 99.9%

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

   3. Taylor expanded in m around 0 0.1%

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

   4. Taylor expanded in v around 0 0.1%

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

      1. mul-1-neg 0.1%

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

      2. unsub-neg 0.1%

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

   6. Simplified 0.1%

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

      1. div-sub 0.1%

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

      2. *-inverses 0.1%

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

      3. sub-neg 0.1%

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

      4. add-sqr-sqrt 0.1%

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

      5. sqrt-unprod 0.1%

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

      6. sqr-neg 0.1%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 77.9%

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

      9. metadata-eval 77.9%

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

      10. +-commutative 77.9%

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

      11. distribute-frac-neg 77.9%

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

      12. unsub-neg 77.9%

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

   8. Applied egg-rr 77.9%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 3.5 \cdot 10^{-186}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 5.6 \cdot 10^{-142}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{elif}\;m \leq 4.2 \cdot 10^{-134}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(-1 - \frac{m}{v}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 3.5 \cdot 10^{-186} \lor \neg \left(m \leq 6.6 \cdot 10^{-142} \lor \neg \left(m \leq 10^{-131}\right) \land m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (or (<= m 3.5e-186)
         (not (or (<= m 6.6e-142) (and (not (<= m 1e-131)) (<= m 1.0)))))
   (- m)
   (* m (/ m v))))

C

double code(double m, double v) {
	double tmp;
	if ((m <= 3.5e-186) || !((m <= 6.6e-142) || (!(m <= 1e-131) && (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 <= 3.5d-186) .or. (.not. (m <= 6.6d-142) .or. (.not. (m <= 1d-131)) .and. (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 <= 3.5e-186) || !((m <= 6.6e-142) || (!(m <= 1e-131) && (m <= 1.0)))) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (m <= 3.5e-186) or not ((m <= 6.6e-142) or (not (m <= 1e-131) and (m <= 1.0))):
		tmp = -m
	else:
		tmp = m * (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if ((m <= 3.5e-186) || !((m <= 6.6e-142) || (!(m <= 1e-131) && (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 <= 3.5e-186) || ~(((m <= 6.6e-142) || (~((m <= 1e-131)) && (m <= 1.0)))))
		tmp = -m;
	else
		tmp = m * (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[Or[LessEqual[m, 3.5e-186], N[Not[Or[LessEqual[m, 6.6e-142], And[N[Not[LessEqual[m, 1e-131]], $MachinePrecision], LessEqual[m, 1.0]]]], $MachinePrecision]], (-m), N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 3.49999999999999989e-186 or 6.5999999999999994e-142 < m < 9.9999999999999999e-132 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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 30.4%

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

      1. neg-mul-1 30.4%

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

   7. Simplified 30.4%

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

   if 3.49999999999999989e-186 < m < 6.5999999999999994e-142 or 9.9999999999999999e-132 < m < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in m around 0 97.1%

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

   4. Taylor expanded in m around inf 64.3%

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

      1. unpow2 64.3%

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

      2. associate-*l/ 76.0%

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

   6. Applied egg-rr 76.0%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 3.5 \cdot 10^{-186} \lor \neg \left(m \leq 6.6 \cdot 10^{-142} \lor \neg \left(m \leq 10^{-131}\right) \land m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. 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* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in m around 0 98.4%

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

      1. div-inv 98.4%

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

      2. clear-num 98.5%

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

   7. Applied egg-rr 98.5%

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

   if 1 < m

   1. Initial program 99.9%

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

   3. Taylor expanded in m around 0 0.1%

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

   4. Taylor expanded in v around 0 0.1%

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

      1. mul-1-neg 0.1%

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

      2. unsub-neg 0.1%

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

   6. Simplified 0.1%

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

      1. div-sub 0.1%

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

      2. *-inverses 0.1%

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

      3. sub-neg 0.1%

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

      4. add-sqr-sqrt 0.1%

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

      5. sqrt-unprod 0.1%

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

      6. sqr-neg 0.1%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 77.9%

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

      9. metadata-eval 77.9%

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

      10. +-commutative 77.9%

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

      11. distribute-frac-neg 77.9%

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

      12. unsub-neg 77.9%

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

   8. Applied egg-rr 77.9%

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

4. Final simplification 88.2%

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

Alternative 5: 97.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. 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* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in m around 0 98.4%

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

      1. div-inv 98.4%

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

      2. clear-num 98.5%

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

   7. Applied egg-rr 98.5%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around inf 98.0%

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

      1. neg-mul-1 98.0%

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

      2. distribute-neg-frac2 98.0%

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

   7. Simplified 98.0%

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

4. Final simplification 98.2%

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

Alternative 6: 87.5% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in m around 0 98.4%

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

   if 1 < m

   1. Initial program 99.9%

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

   3. Taylor expanded in m around 0 0.1%

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

   4. Taylor expanded in v around 0 0.1%

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

      1. mul-1-neg 0.1%

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

      2. unsub-neg 0.1%

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

   6. Simplified 0.1%

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

      1. div-sub 0.1%

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

      2. *-inverses 0.1%

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

      3. sub-neg 0.1%

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

      4. add-sqr-sqrt 0.1%

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

      5. sqrt-unprod 0.1%

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

      6. sqr-neg 0.1%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 77.9%

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

      9. metadata-eval 77.9%

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

      10. +-commutative 77.9%

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

      11. distribute-frac-neg 77.9%

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

      12. unsub-neg 77.9%

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

   8. Applied egg-rr 77.9%

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

4. Final simplification 88.2%

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

Alternative 7: 87.5% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in m around 0 98.4%

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

   4. Taylor expanded in v around 0 98.4%

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

      1. mul-1-neg 98.4%

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

      2. unsub-neg 98.4%

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

   6. Simplified 98.4%

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

      1. *-commutative 98.4%

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

      2. clear-num 98.4%

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

      3. un-div-inv 98.4%

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

   8. Applied egg-rr 98.4%

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

   if 1 < m

   1. Initial program 99.9%

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

   3. Taylor expanded in m around 0 0.1%

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

   4. Taylor expanded in v around 0 0.1%

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

      1. mul-1-neg 0.1%

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

      2. unsub-neg 0.1%

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

   6. Simplified 0.1%

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

      1. div-sub 0.1%

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

      2. *-inverses 0.1%

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

      3. sub-neg 0.1%

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

      4. add-sqr-sqrt 0.1%

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

      5. sqrt-unprod 0.1%

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

      6. sqr-neg 0.1%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 77.9%

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

      9. metadata-eval 77.9%

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

      10. +-commutative 77.9%

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

      11. distribute-frac-neg 77.9%

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

      12. unsub-neg 77.9%

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

   8. Applied egg-rr 77.9%

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

4. Final simplification 88.2%

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

Alternative 8: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-/l* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 9: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-/l* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

   1. clear-num 99.8%

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

   2. un-div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 10: 26.8% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	return -m

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-/l* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in m around 0 27.2%

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

   1. neg-mul-1 27.2%

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

7. Simplified 27.2%

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

8. Final simplification 27.2%

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

Reproduce

herbie shell --seed 2024115 
(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))