a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 6.8s

Alternatives: 10

Speedup: 1.0×

• 41.5% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

   1. associate-/r/ 99.9%

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

   2. div-inv 99.9%

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

   3. associate-/r* 99.9%

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

6. Applied egg-rr 99.9%

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

   1. distribute-rgt-in 99.9%

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

   2. fma-def 99.9%

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

   3. associate-/r/ 99.9%

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

   4. clear-num 99.8%

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

   5. clear-num 99.8%

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

   6. clear-num 99.9%

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

   7. neg-mul-1 99.9%

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

8. Applied egg-rr 99.9%

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

9. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(\frac{m}{v} \cdot \left(1 - m\right), m, -m\right) \]
10. Add Preprocessing

Alternative 2: 37.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 4.6 \cdot 10^{-166} \lor \neg \left(m \leq 5.7 \cdot 10^{-129} \lor \neg \left(m \leq 3.1 \cdot 10^{-103}\right) \land m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (or (<= m 4.6e-166)
         (not (or (<= m 5.7e-129) (and (not (<= m 3.1e-103)) (<= m 1.0)))))
   (- m)
   (* m (/ m v))))

C

double code(double m, double v) {
	double tmp;
	if ((m <= 4.6e-166) || !((m <= 5.7e-129) || (!(m <= 3.1e-103) && (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 <= 4.6d-166) .or. (.not. (m <= 5.7d-129) .or. (.not. (m <= 3.1d-103)) .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 <= 4.6e-166) || !((m <= 5.7e-129) || (!(m <= 3.1e-103) && (m <= 1.0)))) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (m <= 4.6e-166) or not ((m <= 5.7e-129) or (not (m <= 3.1e-103) and (m <= 1.0))):
		tmp = -m
	else:
		tmp = m * (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if ((m <= 4.6e-166) || !((m <= 5.7e-129) || (!(m <= 3.1e-103) && (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 <= 4.6e-166) || ~(((m <= 5.7e-129) || (~((m <= 3.1e-103)) && (m <= 1.0)))))
		tmp = -m;
	else
		tmp = m * (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[Or[LessEqual[m, 4.6e-166], N[Not[Or[LessEqual[m, 5.7e-129], And[N[Not[LessEqual[m, 3.1e-103]], $MachinePrecision], LessEqual[m, 1.0]]]], $MachinePrecision]], (-m), N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 4.59999999999999997e-166 or 5.7000000000000001e-129 < m < 3.1000000000000001e-103 or 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      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 31.2%

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

      1. neg-mul-1 31.2%

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

   7. Simplified 31.2%

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

   if 4.59999999999999997e-166 < m < 5.7000000000000001e-129 or 3.1000000000000001e-103 < m < 1

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l/ 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in m around 0 96.8%

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

   6. Taylor expanded in m around inf 79.6%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 4.6 \cdot 10^{-166} \lor \neg \left(m \leq 5.7 \cdot 10^{-129} \lor \neg \left(m \leq 3.1 \cdot 10^{-103}\right) \land m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.15 \cdot 10^{-44}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{\frac{v}{m}}{1 - m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.15e-44) (* m (+ (/ m v) -1.0)) (/ m (/ (/ v m) (- 1.0 m)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.15e-44) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = m / ((v / m) / (1.0 - m));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 2.15d-44) then
        tmp = m * ((m / v) + (-1.0d0))
    else
        tmp = m / ((v / m) / (1.0d0 - m))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 2.15e-44) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = m / ((v / m) / (1.0 - m));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.15e-44:
		tmp = m * ((m / v) + -1.0)
	else:
		tmp = m / ((v / m) / (1.0 - m))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.15e-44)
		tmp = Float64(m * Float64(Float64(m / v) + -1.0));
	else
		tmp = Float64(m / Float64(Float64(v / m) / Float64(1.0 - m)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.15e-44)
		tmp = m * ((m / v) + -1.0);
	else
		tmp = m / ((v / m) / (1.0 - m));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.15e-44], N[(m * N[(N[(m / v), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(m / N[(N[(v / m), $MachinePrecision] / N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.15000000000000007e-44

   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%

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

   if 2.15000000000000007e-44 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      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 v around 0 99.8%

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

      1. associate-*r/ 99.9%

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

   7. Simplified 99.9%

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

      1. unpow2 99.9%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/r/ 99.9%

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

      5. clear-num 99.8%

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

      6. un-div-inv 99.9%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.15 \cdot 10^{-44}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{\frac{v}{m}}{1 - m}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.15 \cdot 10^{-44}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(1 - m\right)}{\frac{v}{m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.15e-44) (* m (+ (/ m v) -1.0)) (/ (* m (- 1.0 m)) (/ v m))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.15e-44) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = (m * (1.0 - m)) / (v / m);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 2.15d-44) then
        tmp = m * ((m / v) + (-1.0d0))
    else
        tmp = (m * (1.0d0 - m)) / (v / m)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 2.15e-44) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = (m * (1.0 - m)) / (v / m);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.15e-44:
		tmp = m * ((m / v) + -1.0)
	else:
		tmp = (m * (1.0 - m)) / (v / m)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.15e-44)
		tmp = Float64(m * Float64(Float64(m / v) + -1.0));
	else
		tmp = Float64(Float64(m * Float64(1.0 - m)) / Float64(v / m));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.15e-44)
		tmp = m * ((m / v) + -1.0);
	else
		tmp = (m * (1.0 - m)) / (v / m);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.15e-44], N[(m * N[(N[(m / v), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / N[(v / m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.15000000000000007e-44

   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%

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

   if 2.15000000000000007e-44 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      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 v around 0 99.8%

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

      1. associate-*r/ 99.9%

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

   7. Simplified 99.9%

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

      1. unpow2 99.9%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/r/ 99.9%

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

      5. associate-*r/ 99.9%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.15 \cdot 10^{-44}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(1 - m\right)}{\frac{v}{m}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 9 \cdot 10^{-45}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(m \cdot \left(1 - m\right)\right)}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 9e-45) (* m (+ (/ m v) -1.0)) (/ (* m (* m (- 1.0 m))) v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 9e-45) {
		tmp = m * ((m / v) + -1.0);
	} 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 <= 9d-45) then
        tmp = m * ((m / v) + (-1.0d0))
    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 <= 9e-45) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = (m * (m * (1.0 - m))) / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 9e-45:
		tmp = m * ((m / v) + -1.0)
	else:
		tmp = (m * (m * (1.0 - m))) / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 9e-45)
		tmp = Float64(m * Float64(Float64(m / v) + -1.0));
	else
		tmp = Float64(Float64(m * Float64(m * Float64(1.0 - m))) / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 9e-45)
		tmp = m * ((m / v) + -1.0);
	else
		tmp = (m * (m * (1.0 - m))) / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 9e-45], N[(m * N[(N[(m / v), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(m * N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 8.9999999999999997e-45

   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%

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

   if 8.9999999999999997e-45 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      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 v around 0 99.8%

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

      1. associate-*r/ 99.9%

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

   7. Simplified 99.9%

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

      1. unpow2 99.9%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-*r/ 99.9%

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

      5. associate-*l/ 99.9%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 9 \cdot 10^{-45}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(m \cdot \left(1 - m\right)\right)}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.1% 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 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l/ 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in m around 0 98.5%

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

   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/ 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 5.9%

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

      1. neg-mul-1 5.9%

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

   7. Simplified 5.9%

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

4. Final simplification 47.5%

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

Alternative 7: 87.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.0)
		tmp = m * ((m / v) + -1.0);
	else
		tmp = -1.0 / ((v / m) / 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], N[(-1.0 / N[(N[(v / m), $MachinePrecision] / m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l/ 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in m around 0 98.5%

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

   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/ 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 0.1%

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

   6. Taylor expanded in m around inf 0.1%

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

      1. clear-num 0.1%

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

      2. div-inv 0.1%

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

      3. add-sqr-sqrt 0.1%

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

      4. sqrt-prod 0.1%

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

      5. sqr-neg 0.1%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 78.3%

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

      8. neg-mul-1 78.3%

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

      9. associate-/l* 78.3%

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

   8. Applied egg-rr 78.3%

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

4. Final simplification 87.4%

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

Alternative 8: 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 9: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-/l* 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 10: 27.7% 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 28.4%

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

   1. neg-mul-1 28.4%

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

7. Simplified 28.4%

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

8. Final simplification 28.4%

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

Reproduce

herbie shell --seed 2024011 
(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))