a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.6%

Time: 7.3s

Alternatives: 10

Speedup: 1.0×

• 41.8% 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: 99.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.9 \cdot 10^{-25}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(m \cdot \left(1 - m\right)\right)}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.9e-25) (* m (+ (/ m v) -1.0)) (/ (* m (* m (- 1.0 m))) v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.9e-25) {
		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 <= 2.9d-25) 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 <= 2.9e-25) {
		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 <= 2.9e-25:
		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 <= 2.9e-25)
		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 <= 2.9e-25)
		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, 2.9e-25], 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 < 2.9000000000000001e-25

   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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{m}{v}\right)}, 1\right), m\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(m, v\right), 1\right), m\right) \]

   5. Simplified 99.8%

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

   if 2.9000000000000001e-25 < 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 inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto {m}^{3} \cdot \frac{1}{m \cdot v} - \color{blue}{{m}^{3} \cdot \frac{1}{v}} \]

      2. *-commutative N/A

         \[\leadsto {m}^{3} \cdot \frac{1}{m \cdot v} - \frac{1}{v} \cdot \color{blue}{{m}^{3}} \]

      3. fmm-undef N/A

         \[\leadsto \mathsf{fma}\left({m}^{3}, \color{blue}{\frac{1}{m \cdot v}}, \mathsf{neg}\left(\frac{1}{v} \cdot {m}^{3}\right)\right) \]

      4. fma-define N/A

         \[\leadsto {m}^{3} \cdot \frac{1}{m \cdot v} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{v} \cdot {m}^{3}\right)\right)} \]

      5. unpow3 N/A

         \[\leadsto \left(\left(m \cdot m\right) \cdot m\right) \cdot \frac{1}{m \cdot v} + \left(\mathsf{neg}\left(\color{blue}{\frac{1}{v}} \cdot {m}^{3}\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \left({m}^{2} \cdot m\right) \cdot \frac{1}{m \cdot v} + \left(\mathsf{neg}\left(\frac{\color{blue}{1}}{v} \cdot {m}^{3}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto {m}^{2} \cdot \left(m \cdot \frac{1}{m \cdot v}\right) + \left(\mathsf{neg}\left(\color{blue}{\frac{1}{v} \cdot {m}^{3}}\right)\right) \]

      8. fma-define N/A

         \[\leadsto \mathsf{fma}\left({m}^{2}, \color{blue}{m \cdot \frac{1}{m \cdot v}}, \mathsf{neg}\left(\frac{1}{v} \cdot {m}^{3}\right)\right) \]

      9. associate-/r* N/A

         \[\leadsto \mathsf{fma}\left({m}^{2}, m \cdot \frac{\frac{1}{m}}{\color{blue}{v}}, \mathsf{neg}\left(\frac{1}{v} \cdot {m}^{3}\right)\right) \]

      10. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left({m}^{2}, \frac{m \cdot \frac{1}{m}}{\color{blue}{v}}, \mathsf{neg}\left(\frac{1}{v} \cdot {m}^{3}\right)\right) \]

      11. rgt-mult-inverse N/A

          \[\leadsto \mathsf{fma}\left({m}^{2}, \frac{1}{v}, \mathsf{neg}\left(\frac{1}{v} \cdot {m}^{3}\right)\right) \]

      12. fmm-undef N/A

          \[\leadsto {m}^{2} \cdot \frac{1}{v} - \color{blue}{\frac{1}{v} \cdot {m}^{3}} \]

      13. *-commutative N/A

          \[\leadsto {m}^{2} \cdot \frac{1}{v} - {m}^{3} \cdot \color{blue}{\frac{1}{v}} \]

      14. unpow3 N/A

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

      15. unpow2 N/A

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

      16. associate-*l* N/A

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

      17. associate-*r/ N/A

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

      18. *-rgt-identity N/A

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.9 \cdot 10^{-25}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(m \cdot \left(1 - m\right)\right)}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.8 \cdot 10^{-24}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.8e-24) (* m (+ (/ m v) -1.0)) (/ m (/ v (* m (- 1.0 m))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.8e-24) {
		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 <= 2.8d-24) 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 <= 2.8e-24) {
		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 <= 2.8e-24:
		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 <= 2.8e-24)
		tmp = Float64(m * Float64(Float64(m / v) + -1.0));
	else
		tmp = Float64(m / Float64(v / Float64(m * Float64(1.0 - m))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.8e-24)
		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, 2.8e-24], N[(m * N[(N[(m / v), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(m / N[(v / N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.8000000000000002e-24

   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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{m}{v}\right)}, 1\right), m\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(m, v\right), 1\right), m\right) \]

   5. Simplified 99.8%

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

   if 2.8000000000000002e-24 < 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 inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left({m}^{2} \cdot \left(\frac{1}{m \cdot v} - \frac{1}{v}\right)\right)}, m\right) \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - {m}^{2} \cdot \frac{1}{v}\right), m\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - \left(m \cdot m\right) \cdot \frac{1}{v}\right), m\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - m \cdot \left(m \cdot \frac{1}{v}\right)\right), m\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - m \cdot \frac{m \cdot 1}{v}\right), m\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - m \cdot \frac{m}{v}\right), m\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(m \cdot m\right) \cdot \frac{1}{m \cdot v} - m \cdot \frac{m}{v}\right), m\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \left(m \cdot \frac{1}{m \cdot v}\right) - m \cdot \frac{m}{v}\right), m\right) \]

      8. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \left(m \cdot \frac{1}{m \cdot v}\right) - \frac{m \cdot m}{v}\right), m\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \left(m \cdot \frac{1}{m \cdot v}\right) - \frac{{m}^{2}}{v}\right), m\right) \]

      10. fmm-def N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{fma}\left(m, m \cdot \frac{1}{m \cdot v}, \mathsf{neg}\left(\frac{{m}^{2}}{v}\right)\right)\right), m\right) \]

      11. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{fma}\left(m, m \cdot \frac{\frac{1}{m}}{v}, \mathsf{neg}\left(\frac{{m}^{2}}{v}\right)\right)\right), m\right) \]

      12. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{fma}\left(m, \frac{m \cdot \frac{1}{m}}{v}, \mathsf{neg}\left(\frac{{m}^{2}}{v}\right)\right)\right), m\right) \]

      13. rgt-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{fma}\left(m, \frac{1}{v}, \mathsf{neg}\left(\frac{{m}^{2}}{v}\right)\right)\right), m\right) \]

      14. fmm-def N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1}{v} - \frac{{m}^{2}}{v}\right), m\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1}{v} - \frac{m \cdot m}{v}\right), m\right) \]

      16. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1}{v} - m \cdot \frac{m}{v}\right), m\right) \]

      17. distribute-lft-out-- N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \left(\frac{1}{v} - \frac{m}{v}\right)\right), m\right) \]

      18. div-sub N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1 - m}{v}\right), m\right) \]

      19. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{m \cdot \left(1 - m\right)}{v}\right), m\right) \]

      20. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(m \cdot \left(1 - m\right)\right), v\right), m\right) \]

   5. Simplified 99.9%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. associate-/l/ N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(m, \color{blue}{\left(\frac{\frac{v}{1 - m}}{m}\right)}\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{/.f64}\left(m, \left(\frac{v}{\color{blue}{m \cdot \left(1 - m\right)}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(m, \mathsf{/.f64}\left(v, \color{blue}{\left(m \cdot \left(1 - m\right)\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(m, \mathsf{/.f64}\left(v, \mathsf{*.f64}\left(m, \color{blue}{\left(1 - m\right)}\right)\right)\right) \]

      9. --lowering--.f64 99.9%

         \[\leadsto \mathsf{/.f64}\left(m, \mathsf{/.f64}\left(v, \mathsf{*.f64}\left(m, \mathsf{\_.f64}\left(1, \color{blue}{m}\right)\right)\right)\right) \]

   7. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.8 \cdot 10^{-24}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.65 \cdot 10^{-31}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(m \cdot \frac{1 - m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.65e-31) (* m (+ (/ m v) -1.0)) (* m (* m (/ (- 1.0 m) v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.65e-31) {
		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 <= 1.65d-31) 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 <= 1.65e-31) {
		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 <= 1.65e-31:
		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 <= 1.65e-31)
		tmp = Float64(m * Float64(Float64(m / v) + -1.0));
	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 <= 1.65e-31)
		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, 1.65e-31], N[(m * N[(N[(m / v), $MachinePrecision] + -1.0), $MachinePrecision]), $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 < 1.65e-31

   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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{m}{v}\right)}, 1\right), m\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(m, v\right), 1\right), m\right) \]

   5. Simplified 99.8%

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

   if 1.65e-31 < 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 inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left({m}^{2} \cdot \left(\frac{1}{m \cdot v} - \frac{1}{v}\right)\right)}, m\right) \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - {m}^{2} \cdot \frac{1}{v}\right), m\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - \left(m \cdot m\right) \cdot \frac{1}{v}\right), m\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - m \cdot \left(m \cdot \frac{1}{v}\right)\right), m\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - m \cdot \frac{m \cdot 1}{v}\right), m\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - m \cdot \frac{m}{v}\right), m\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(m \cdot m\right) \cdot \frac{1}{m \cdot v} - m \cdot \frac{m}{v}\right), m\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \left(m \cdot \frac{1}{m \cdot v}\right) - m \cdot \frac{m}{v}\right), m\right) \]

      8. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \left(m \cdot \frac{1}{m \cdot v}\right) - \frac{m \cdot m}{v}\right), m\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \left(m \cdot \frac{1}{m \cdot v}\right) - \frac{{m}^{2}}{v}\right), m\right) \]

      10. fmm-def N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{fma}\left(m, m \cdot \frac{1}{m \cdot v}, \mathsf{neg}\left(\frac{{m}^{2}}{v}\right)\right)\right), m\right) \]

      11. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{fma}\left(m, m \cdot \frac{\frac{1}{m}}{v}, \mathsf{neg}\left(\frac{{m}^{2}}{v}\right)\right)\right), m\right) \]

      12. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{fma}\left(m, \frac{m \cdot \frac{1}{m}}{v}, \mathsf{neg}\left(\frac{{m}^{2}}{v}\right)\right)\right), m\right) \]

      13. rgt-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{fma}\left(m, \frac{1}{v}, \mathsf{neg}\left(\frac{{m}^{2}}{v}\right)\right)\right), m\right) \]

      14. fmm-def N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1}{v} - \frac{{m}^{2}}{v}\right), m\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1}{v} - \frac{m \cdot m}{v}\right), m\right) \]

      16. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1}{v} - m \cdot \frac{m}{v}\right), m\right) \]

      17. distribute-lft-out-- N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \left(\frac{1}{v} - \frac{m}{v}\right)\right), m\right) \]

      18. div-sub N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1 - m}{v}\right), m\right) \]

      19. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{m \cdot \left(1 - m\right)}{v}\right), m\right) \]

      20. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(m \cdot \left(1 - m\right)\right), v\right), m\right) \]

   5. Simplified 99.9%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1 - m}{v}\right), m\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1 - m}{v} \cdot m\right), m\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1 - m}{v}\right), m\right), m\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(1 - m\right), v\right), m\right), m\right) \]

      5. --lowering--.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, m\right), v\right), m\right), m\right) \]

   7. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.65 \cdot 10^{-31}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(m \cdot \frac{1 - m}{v}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0 - m \cdot m}{m}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.0) (* m (+ (/ m v) -1.0)) (/ (- 0.0 (* m m)) m)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.0) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = (0.0 - (m * 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 = (0.0d0 - (m * 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 = (0.0 - (m * m)) / m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.0:
		tmp = m * ((m / v) + -1.0)
	else:
		tmp = (0.0 - (m * 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(Float64(0.0 - Float64(m * 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 = (0.0 - (m * 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[(N[(0.0 - N[(m * m), $MachinePrecision]), $MachinePrecision] / m), $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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{m}{v}\right)}, 1\right), m\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 98.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(m, v\right), 1\right), m\right) \]

   5. Simplified 98.8%

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

   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

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(m\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{m} \]

      3. --lowering--.f64 5.7%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{m}\right) \]

   5. Simplified 5.7%

      \[\leadsto \color{blue}{0 - m} \]
   6. Step-by-step derivation

      1. flip-- N/A

         \[\leadsto \frac{0 \cdot 0 - m \cdot m}{\color{blue}{0 + m}} \]

      2. +-lft-identity N/A

         \[\leadsto \frac{0 \cdot 0 - m \cdot m}{m} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(0 \cdot 0 - m \cdot m\right), \color{blue}{m}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(0 - m \cdot m\right), m\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(m \cdot m\right)\right), m\right) \]

      6. *-lowering-*.f64 53.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(m, m\right)\right), m\right) \]

   7. Applied egg-rr 53.4%

      \[\leadsto \color{blue}{\frac{0 - m \cdot m}{m}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0 - m \cdot m}{m}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.6% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Python

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{m}{v}\right)}, 1\right), m\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 98.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(m, v\right), 1\right), m\right) \]

   5. Simplified 98.8%

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

   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

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(m\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{m} \]

      3. --lowering--.f64 5.7%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{m}\right) \]

   5. Simplified 5.7%

      \[\leadsto \color{blue}{0 - m} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(m\right) \]

      2. neg-mul-1 N/A

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

      3. remove-double-div N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \color{blue}{\left(\frac{1}{m}\right)}\right) \]

      6. /-lowering-/.f64 5.7%

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{/.f64}\left(1, \color{blue}{m}\right)\right) \]

   7. Applied egg-rr 5.7%

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

4. Final simplification 57.0%

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

Alternative 6: 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. Add Preprocessing

3. Final simplification 99.8%

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

Alternative 7: 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. Add Preprocessing
3. Step-by-step derivation

   1. associate-/l* N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(m \cdot \frac{1 - m}{v}\right), 1\right), m\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{1 - m}{v} \cdot m\right), 1\right), m\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\frac{1 - m}{v}\right), m\right), 1\right), m\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(1 - m\right), v\right), m\right), 1\right), m\right) \]

   5. --lowering--.f64 99.7%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, m\right), v\right), m\right), 1\right), m\right) \]

4. Applied egg-rr 99.7%

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

5. Final simplification 99.7%

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

Alternative 8: 38.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 2.65 \cdot 10^{-151}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;0 - m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= v 2.65e-151) (/ m (/ v m)) (- 0.0 m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 2.65e-151) {
		tmp = m / (v / m);
	} else {
		tmp = 0.0 - m;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (v <= 2.65d-151) then
        tmp = m / (v / m)
    else
        tmp = 0.0d0 - m
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (v <= 2.65e-151) {
		tmp = m / (v / m);
	} else {
		tmp = 0.0 - m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 2.65e-151:
		tmp = m / (v / m)
	else:
		tmp = 0.0 - m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 2.65e-151)
		tmp = Float64(m / Float64(v / m));
	else
		tmp = Float64(0.0 - m);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (v <= 2.65e-151)
		tmp = m / (v / m);
	else
		tmp = 0.0 - m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 2.65e-151], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], N[(0.0 - m), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if v < 2.64999999999999989e-151

   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 inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left({m}^{2} \cdot \left(\frac{1}{m \cdot v} - \frac{1}{v}\right)\right)}, m\right) \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - {m}^{2} \cdot \frac{1}{v}\right), m\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - \left(m \cdot m\right) \cdot \frac{1}{v}\right), m\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - m \cdot \left(m \cdot \frac{1}{v}\right)\right), m\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - m \cdot \frac{m \cdot 1}{v}\right), m\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{*.f64}\left(\left({m}^{2} \cdot \frac{1}{m \cdot v} - m \cdot \frac{m}{v}\right), m\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(m \cdot m\right) \cdot \frac{1}{m \cdot v} - m \cdot \frac{m}{v}\right), m\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \left(m \cdot \frac{1}{m \cdot v}\right) - m \cdot \frac{m}{v}\right), m\right) \]

      8. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \left(m \cdot \frac{1}{m \cdot v}\right) - \frac{m \cdot m}{v}\right), m\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \left(m \cdot \frac{1}{m \cdot v}\right) - \frac{{m}^{2}}{v}\right), m\right) \]

      10. fmm-def N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{fma}\left(m, m \cdot \frac{1}{m \cdot v}, \mathsf{neg}\left(\frac{{m}^{2}}{v}\right)\right)\right), m\right) \]

      11. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{fma}\left(m, m \cdot \frac{\frac{1}{m}}{v}, \mathsf{neg}\left(\frac{{m}^{2}}{v}\right)\right)\right), m\right) \]

      12. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{fma}\left(m, \frac{m \cdot \frac{1}{m}}{v}, \mathsf{neg}\left(\frac{{m}^{2}}{v}\right)\right)\right), m\right) \]

      13. rgt-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{fma}\left(m, \frac{1}{v}, \mathsf{neg}\left(\frac{{m}^{2}}{v}\right)\right)\right), m\right) \]

      14. fmm-def N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1}{v} - \frac{{m}^{2}}{v}\right), m\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1}{v} - \frac{m \cdot m}{v}\right), m\right) \]

      16. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1}{v} - m \cdot \frac{m}{v}\right), m\right) \]

      17. distribute-lft-out-- N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \left(\frac{1}{v} - \frac{m}{v}\right)\right), m\right) \]

      18. div-sub N/A

          \[\leadsto \mathsf{*.f64}\left(\left(m \cdot \frac{1 - m}{v}\right), m\right) \]

      19. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{m \cdot \left(1 - m\right)}{v}\right), m\right) \]

      20. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(m \cdot \left(1 - m\right)\right), v\right), m\right) \]

   5. Simplified 88.8%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. associate-/l/ N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(m, \color{blue}{\left(\frac{\frac{v}{1 - m}}{m}\right)}\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{/.f64}\left(m, \left(\frac{v}{\color{blue}{m \cdot \left(1 - m\right)}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(m, \mathsf{/.f64}\left(v, \color{blue}{\left(m \cdot \left(1 - m\right)\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(m, \mathsf{/.f64}\left(v, \mathsf{*.f64}\left(m, \color{blue}{\left(1 - m\right)}\right)\right)\right) \]

      9. --lowering--.f64 88.9%

         \[\leadsto \mathsf{/.f64}\left(m, \mathsf{/.f64}\left(v, \mathsf{*.f64}\left(m, \mathsf{\_.f64}\left(1, \color{blue}{m}\right)\right)\right)\right) \]

   7. Applied egg-rr 88.9%

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

   8. Taylor expanded in m around 0

      \[\leadsto \mathsf{/.f64}\left(m, \color{blue}{\left(\frac{v}{m}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 43.0%

         \[\leadsto \mathsf{/.f64}\left(m, \mathsf{/.f64}\left(v, \color{blue}{m}\right)\right) \]

   10. Simplified 43.0%

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

   if 2.64999999999999989e-151 < v

   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

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(m\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{m} \]

      3. --lowering--.f64 50.8%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{m}\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{0 - m} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(m\right) \]

      2. neg-lowering-neg.f64 50.8%

         \[\leadsto \mathsf{neg.f64}\left(m\right) \]

   7. Applied egg-rr 50.8%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq 2.65 \cdot 10^{-151}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;0 - m\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 2.95 \cdot 10^{-151}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;0 - m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= v 2.95e-151) (* m (/ m v)) (- 0.0 m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 2.95e-151) {
		tmp = m * (m / v);
	} else {
		tmp = 0.0 - m;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (v <= 2.95d-151) then
        tmp = m * (m / v)
    else
        tmp = 0.0d0 - m
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (v <= 2.95e-151) {
		tmp = m * (m / v);
	} else {
		tmp = 0.0 - m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 2.95e-151:
		tmp = m * (m / v)
	else:
		tmp = 0.0 - m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 2.95e-151)
		tmp = Float64(m * Float64(m / v));
	else
		tmp = Float64(0.0 - m);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (v <= 2.95e-151)
		tmp = m * (m / v);
	else
		tmp = 0.0 - m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 2.95e-151], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], N[(0.0 - m), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if v < 2.95e-151

   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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{m}{v}\right)}, 1\right), m\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 53.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(m, v\right), 1\right), m\right) \]

   5. Simplified 53.9%

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

   6. Taylor expanded in m around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{m}{v}\right)}, m\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 43.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(m, v\right), m\right) \]

   8. Simplified 43.0%

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

   if 2.95e-151 < v

   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

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(m\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{m} \]

      3. --lowering--.f64 50.8%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{m}\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{0 - m} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(m\right) \]

      2. neg-lowering-neg.f64 50.8%

         \[\leadsto \mathsf{neg.f64}\left(m\right) \]

   7. Applied egg-rr 50.8%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq 2.95 \cdot 10^{-151}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;0 - m\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 27.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ 0 - m \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (- 0.0 m))

C

double code(double m, double v) {
	return 0.0 - m;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    code = 0.0d0 - m
end function

Java

public static double code(double m, double v) {
	return 0.0 - m;
}

Python

def code(m, v):
	return 0.0 - m

Julia

function code(m, v)
	return Float64(0.0 - m)
end

MATLAB

function tmp = code(m, v)
	tmp = 0.0 - m;
end

Wolfram

code[m_, v_] := N[(0.0 - m), $MachinePrecision]

Derivation

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

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(m\right) \]

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{m} \]

   3. --lowering--.f64 29.5%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{m}\right) \]

5. Simplified 29.5%

   \[\leadsto \color{blue}{0 - m} \]
6. Step-by-step derivation

   1. sub0-neg N/A

      \[\leadsto \mathsf{neg}\left(m\right) \]

   2. neg-lowering-neg.f64 29.5%

      \[\leadsto \mathsf{neg.f64}\left(m\right) \]

7. Applied egg-rr 29.5%

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

8. Final simplification 29.5%

   \[\leadsto 0 - m \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024139 
(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))