a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 5.5s

Alternatives: 12

Speedup: 1.0×

• 41.3% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   4. associate-/l* 99.8%

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

   5. associate-/r/ 99.8%

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

   6. metadata-eval 99.8%

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

   7. neg-mul-1 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 37.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 1.8 \cdot 10^{-180} \lor \neg \left(v \leq 1.4 \cdot 10^{-156}\right) \land v \leq 5.1 \cdot 10^{-151}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (or (<= v 1.8e-180) (and (not (<= v 1.4e-156)) (<= v 5.1e-151)))
   (* m (/ m v))
   (- m)))

C

double code(double m, double v) {
	double tmp;
	if ((v <= 1.8e-180) || (!(v <= 1.4e-156) && (v <= 5.1e-151))) {
		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 <= 1.8d-180) .or. (.not. (v <= 1.4d-156)) .and. (v <= 5.1d-151)) 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 <= 1.8e-180) || (!(v <= 1.4e-156) && (v <= 5.1e-151))) {
		tmp = m * (m / v);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (v <= 1.8e-180) or (not (v <= 1.4e-156) and (v <= 5.1e-151)):
		tmp = m * (m / v)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if ((v <= 1.8e-180) || (!(v <= 1.4e-156) && (v <= 5.1e-151)))
		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 <= 1.8e-180) || (~((v <= 1.4e-156)) && (v <= 5.1e-151)))
		tmp = m * (m / v);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[Or[LessEqual[v, 1.8e-180], And[N[Not[LessEqual[v, 1.4e-156]], $MachinePrecision], LessEqual[v, 5.1e-151]]], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], (-m)]

Derivation

1. Split input into 2 regimes

2. if v < 1.8e-180 or 1.4000000000000001e-156 < v < 5.0999999999999997e-151

   1. Initial program 99.7%

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

   2. Taylor expanded in v around 0 90.4%

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

   3. Taylor expanded in m around 0 48.0%

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

   if 1.8e-180 < v < 1.4000000000000001e-156 or 5.0999999999999997e-151 < v

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 43.4%

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

      1. neg-mul-1 43.4%

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

   4. Simplified 43.4%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq 1.8 \cdot 10^{-180} \lor \neg \left(v \leq 1.4 \cdot 10^{-156}\right) \land v \leq 5.1 \cdot 10^{-151}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 3: 37.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 2.7 \cdot 10^{-180} \lor \neg \left(v \leq 1.06 \cdot 10^{-156}\right) \land v \leq 5.1 \cdot 10^{-151}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (or (<= v 2.7e-180) (and (not (<= v 1.06e-156)) (<= v 5.1e-151)))
   (/ m (/ v m))
   (- m)))

C

double code(double m, double v) {
	double tmp;
	if ((v <= 2.7e-180) || (!(v <= 1.06e-156) && (v <= 5.1e-151))) {
		tmp = m / (v / m);
	} 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 <= 2.7d-180) .or. (.not. (v <= 1.06d-156)) .and. (v <= 5.1d-151)) then
        tmp = m / (v / m)
    else
        tmp = -m
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if ((v <= 2.7e-180) || (!(v <= 1.06e-156) && (v <= 5.1e-151))) {
		tmp = m / (v / m);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (v <= 2.7e-180) or (not (v <= 1.06e-156) and (v <= 5.1e-151)):
		tmp = m / (v / m)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if ((v <= 2.7e-180) || (!(v <= 1.06e-156) && (v <= 5.1e-151)))
		tmp = Float64(m / Float64(v / m));
	else
		tmp = Float64(-m);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if ((v <= 2.7e-180) || (~((v <= 1.06e-156)) && (v <= 5.1e-151)))
		tmp = m / (v / m);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[Or[LessEqual[v, 2.7e-180], And[N[Not[LessEqual[v, 1.06e-156]], $MachinePrecision], LessEqual[v, 5.1e-151]]], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], (-m)]

Derivation

1. Split input into 2 regimes

2. if v < 2.70000000000000014e-180 or 1.06e-156 < v < 5.0999999999999997e-151

   1. Initial program 99.7%

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

   2. Taylor expanded in v around 0 90.4%

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

   3. Taylor expanded in m around 0 48.0%

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

      1. associate-/r/ 48.0%

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

   5. Applied egg-rr 48.0%

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

   if 2.70000000000000014e-180 < v < 1.06e-156 or 5.0999999999999997e-151 < v

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 43.4%

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

      1. neg-mul-1 43.4%

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

   4. Simplified 43.4%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq 2.7 \cdot 10^{-180} \lor \neg \left(v \leq 1.06 \cdot 10^{-156}\right) \land v \leq 5.1 \cdot 10^{-151}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]

Alternative 4: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.42 \cdot 10^{-11}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(m \cdot \frac{1 - m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.42e-11) (- (* m (/ m v)) m) (* m (* m (/ (- 1.0 m) v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.42e-11) {
		tmp = (m * (m / v)) - m;
	} else {
		tmp = m * (m * ((1.0 - m) / v));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.42d-11) then
        tmp = (m * (m / v)) - m
    else
        tmp = m * (m * ((1.0d0 - m) / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.42e-11) {
		tmp = (m * (m / v)) - m;
	} else {
		tmp = m * (m * ((1.0 - m) / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.42e-11:
		tmp = (m * (m / v)) - m
	else:
		tmp = m * (m * ((1.0 - m) / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.42e-11)
		tmp = Float64(Float64(m * Float64(m / v)) - m);
	else
		tmp = Float64(m * Float64(m * Float64(Float64(1.0 - m) / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.42e-11)
		tmp = (m * (m / v)) - m;
	else
		tmp = m * (m * ((1.0 - m) / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.42e-11], N[(N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision], N[(m * N[(m * N[(N[(1.0 - m), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.42e-11

   1. Initial program 99.7%

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

   2. Taylor expanded in m around 0 86.9%

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

      1. neg-mul-1 86.9%

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

      2. +-commutative 86.9%

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

      3. unsub-neg 86.9%

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

   4. Simplified 86.9%

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

      1. div-inv 86.9%

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

      2. unpow2 86.9%

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

      3. associate-*l* 99.4%

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

      4. div-inv 99.4%

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

   6. Applied egg-rr 99.4%

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

   if 1.42e-11 < m

   1. Initial program 100.0%

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

   2. Taylor expanded in v around 0 100.0%

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

   3. Taylor expanded in m around 0 52.0%

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

      1. +-commutative 52.0%

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

      2. *-lft-identity 52.0%

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

      3. mul-1-neg 52.0%

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

      4. unpow2 52.0%

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

      5. associate-*r/ 52.0%

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

      6. distribute-lft-neg-in 52.0%

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

      7. distribute-rgt-in 100.0%

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

      8. sub-neg 100.0%

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

      9. associate-*l/ 100.0%

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

      10. associate-*r/ 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.42 \cdot 10^{-11}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(m \cdot \frac{1 - m}{v}\right)\\ \end{array} \]

Alternative 5: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.42 \cdot 10^{-11}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m \cdot \left(1 - m\right)}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.42e-11) (- (* m (/ m v)) m) (* m (/ (* m (- 1.0 m)) v))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.42e-11) {
		tmp = (m * (m / v)) - m;
	} else {
		tmp = m * ((m * (1.0 - m)) / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.42d-11) then
        tmp = (m * (m / v)) - m
    else
        tmp = m * ((m * (1.0d0 - m)) / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.42e-11) {
		tmp = (m * (m / v)) - m;
	} else {
		tmp = m * ((m * (1.0 - m)) / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.42e-11:
		tmp = (m * (m / v)) - m
	else:
		tmp = m * ((m * (1.0 - m)) / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.42e-11)
		tmp = Float64(Float64(m * Float64(m / v)) - m);
	else
		tmp = Float64(m * Float64(Float64(m * Float64(1.0 - m)) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.42e-11)
		tmp = (m * (m / v)) - m;
	else
		tmp = m * ((m * (1.0 - m)) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.42e-11], N[(N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision], N[(m * N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.42e-11

   1. Initial program 99.7%

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

   2. Taylor expanded in m around 0 86.9%

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

      1. neg-mul-1 86.9%

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

      2. +-commutative 86.9%

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

      3. unsub-neg 86.9%

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

   4. Simplified 86.9%

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

      1. div-inv 86.9%

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

      2. unpow2 86.9%

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

      3. associate-*l* 99.4%

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

      4. div-inv 99.4%

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

   6. Applied egg-rr 99.4%

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

   if 1.42e-11 < m

   1. Initial program 100.0%

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

   2. Taylor expanded in v around 0 100.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.42 \cdot 10^{-11}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m \cdot \left(1 - m\right)}{v}\\ \end{array} \]

Alternative 6: 99.8% accurate, 1.0× speedup

Math

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

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(m * Float64(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[(m * N[(N[(1.0 - m), $MachinePrecision] / v), $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. Taylor expanded in m around 0 77.6%

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

   1. +-commutative 50.8%

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

   2. *-lft-identity 50.8%

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

   3. mul-1-neg 50.8%

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

   4. unpow2 50.8%

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

   5. associate-*r/ 50.8%

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

   6. distribute-lft-neg-in 50.8%

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

   7. distribute-rgt-in 73.0%

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

   8. sub-neg 73.0%

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

   9. associate-*l/ 73.0%

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

   10. associate-*r/ 73.0%

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

4. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 7: 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 8: 97.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

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

   2. Taylor expanded in m around 0 86.1%

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

      1. neg-mul-1 86.1%

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

      2. +-commutative 86.1%

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

      3. unsub-neg 86.1%

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

   4. Simplified 86.1%

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

      1. div-inv 86.0%

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

      2. unpow2 86.0%

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

      3. associate-*l* 98.2%

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

      4. div-inv 98.2%

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

   6. Applied egg-rr 98.2%

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

   if 1 < m

   1. Initial program 100.0%

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

   2. Taylor expanded in v around 0 100.0%

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

   3. Taylor expanded in m around 0 50.4%

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

      1. +-commutative 50.4%

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

      2. *-lft-identity 50.4%

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

      3. mul-1-neg 50.4%

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

      4. unpow2 50.4%

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

      5. associate-*r/ 50.4%

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

      6. distribute-lft-neg-in 50.4%

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

      7. distribute-rgt-in 100.0%

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

      8. sub-neg 100.0%

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

      9. associate-*l/ 100.0%

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

      10. associate-*r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in m around inf 99.5%

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

      1. associate-*r/ 99.5%

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

      2. mul-1-neg 99.5%

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

   8. Simplified 99.5%

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

4. Final simplification 98.8%

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

Alternative 9: 52.3% accurate, 1.2× 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 99.7%

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

   2. Taylor expanded in m around 0 98.1%

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

   if 1 < m

   1. Initial program 100.0%

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

   2. Taylor expanded in m around 0 5.4%

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

      1. neg-mul-1 5.4%

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

   4. Simplified 5.4%

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

4. Final simplification 56.5%

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

Alternative 10: 52.3% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

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

   2. Taylor expanded in m around 0 86.1%

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

      1. neg-mul-1 86.1%

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

      2. +-commutative 86.1%

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

      3. unsub-neg 86.1%

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

   4. Simplified 86.1%

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

      1. div-inv 86.0%

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

      2. unpow2 86.0%

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

      3. associate-*l* 98.2%

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

      4. div-inv 98.2%

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

   6. Applied egg-rr 98.2%

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

   if 1 < m

   1. Initial program 100.0%

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

   2. Taylor expanded in m around 0 5.4%

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

      1. neg-mul-1 5.4%

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

   4. Simplified 5.4%

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

4. Final simplification 56.5%

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

Alternative 11: 88.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

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

   2. Taylor expanded in m around 0 86.1%

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

      1. neg-mul-1 86.1%

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

      2. +-commutative 86.1%

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

      3. unsub-neg 86.1%

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

   4. Simplified 86.1%

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

      1. div-inv 86.0%

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

      2. unpow2 86.0%

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

      3. associate-*l* 98.2%

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

      4. div-inv 98.2%

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

   6. Applied egg-rr 98.2%

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

   if 1 < m

   1. Initial program 100.0%

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

   2. Taylor expanded in v around 0 100.0%

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

   3. Taylor expanded in m around 0 0.0%

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

      1. *-commutative 0.0%

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

      2. clear-num 0.0%

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

      3. *-un-lft-identity 0.0%

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

      4. associate-*l/ 0.0%

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

      5. frac-2neg 0.0%

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

      6. metadata-eval 0.0%

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

      7. associate-*r/ 0.0%

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

      8. associate-*l/ 0.0%

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

      9. *-un-lft-identity 0.0%

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

      10. distribute-neg-frac 0.0%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 0.0%

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

      13. sqr-neg 0.0%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 80.3%

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

      16. frac-2neg 80.3%

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

   5. Applied egg-rr 80.3%

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

4. Final simplification 90.2%

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

Alternative 12: 27.9% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	return -m

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in m around 0 29.3%

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

   1. neg-mul-1 29.3%

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

4. Simplified 29.3%

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

5. Final simplification 29.3%

   \[\leadsto -m \]

Reproduce

herbie shell --seed 2023339 
(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))