a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 7.7s

Alternatives: 10

Speedup: 1.1×

• 42.1% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. *-commutative N/A

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

   6. lift--.f64 N/A

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

   7. sub-neg N/A

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

   8. distribute-lft-in N/A

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

   9. lift-/.f64 N/A

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

   10. lift-*.f64 N/A

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

   11. *-commutative N/A

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

   12. associate-/l* N/A

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

   13. associate-*r* N/A

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

   14. lift-*.f64 N/A

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

   15. distribute-rgt-neg-in N/A

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

   16. *-rgt-identity N/A

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

   17. lower-fma.f64 N/A

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

4. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(m, -m, m\right), \frac{m}{v}, -m\right)} \]
5. Add Preprocessing

Alternative 2: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := m \cdot \left(-1 + \frac{m \cdot \left(1 - m\right)}{v}\right)\\ t_1 := m \cdot \frac{m}{v}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+33}:\\ \;\;\;\;-t\_1\\ \mathbf{elif}\;t\_0 \leq -1 \cdot 10^{-308}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (let* ((t_0 (* m (+ -1.0 (/ (* m (- 1.0 m)) v)))) (t_1 (* m (/ m v))))
   (if (<= t_0 -5e+33) (- t_1) (if (<= t_0 -1e-308) (- m) t_1))))

C

double code(double m, double v) {
	double t_0 = m * (-1.0 + ((m * (1.0 - m)) / v));
	double t_1 = m * (m / v);
	double tmp;
	if (t_0 <= -5e+33) {
		tmp = -t_1;
	} else if (t_0 <= -1e-308) {
		tmp = -m;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = m * ((-1.0d0) + ((m * (1.0d0 - m)) / v))
    t_1 = m * (m / v)
    if (t_0 <= (-5d+33)) then
        tmp = -t_1
    else if (t_0 <= (-1d-308)) then
        tmp = -m
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double t_0 = m * (-1.0 + ((m * (1.0 - m)) / v));
	double t_1 = m * (m / v);
	double tmp;
	if (t_0 <= -5e+33) {
		tmp = -t_1;
	} else if (t_0 <= -1e-308) {
		tmp = -m;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(m, v):
	t_0 = m * (-1.0 + ((m * (1.0 - m)) / v))
	t_1 = m * (m / v)
	tmp = 0
	if t_0 <= -5e+33:
		tmp = -t_1
	elif t_0 <= -1e-308:
		tmp = -m
	else:
		tmp = t_1
	return tmp

Julia

function code(m, v)
	t_0 = Float64(m * Float64(-1.0 + Float64(Float64(m * Float64(1.0 - m)) / v)))
	t_1 = Float64(m * Float64(m / v))
	tmp = 0.0
	if (t_0 <= -5e+33)
		tmp = Float64(-t_1);
	elseif (t_0 <= -1e-308)
		tmp = Float64(-m);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	t_0 = m * (-1.0 + ((m * (1.0 - m)) / v));
	t_1 = m * (m / v);
	tmp = 0.0;
	if (t_0 <= -5e+33)
		tmp = -t_1;
	elseif (t_0 <= -1e-308)
		tmp = -m;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := Block[{t$95$0 = N[(m * N[(-1.0 + N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+33], (-t$95$1), If[LessEqual[t$95$0, -1e-308], (-m), t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m) < -4.99999999999999973e33

   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

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

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

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

      2. unpow2 N/A

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

      3. associate-*l* N/A

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

      4. associate-/r* N/A

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

      5. associate-*r/ N/A

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

      6. rgt-mult-inverse N/A

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

      7. unpow2 N/A

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

      8. associate-*r* N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

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

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

      12. div-sub N/A

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

      13. associate-/l* N/A

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

      14. lower-/.f64 N/A

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

      15. distribute-rgt-out-- N/A

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

      16. *-lft-identity N/A

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

      17. unpow2 N/A

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

      18. lower--.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 99.9

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

   5. Simplified 99.9%

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

   6. Taylor expanded in m around 0

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

      1. lower-/.f64 0.1

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

   8. Simplified 0.1%

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

   10. Applied egg-rr 82.1%

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

   if -4.99999999999999973e33 < (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m) < -9.9999999999999991e-309

   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

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

      2. lower-neg.f64 91.7

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

   5. Simplified 91.7%

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

   if -9.9999999999999991e-309 < (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m)

   1. Initial program 99.5%

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

   3. Taylor expanded in m around inf

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

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

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

      2. unpow2 N/A

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

      3. associate-*l* N/A

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

      4. associate-/r* N/A

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

      5. associate-*r/ N/A

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

      6. rgt-mult-inverse N/A

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

      7. unpow2 N/A

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

      8. associate-*r* N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

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

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

      12. div-sub N/A

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

      13. associate-/l* N/A

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

      14. lower-/.f64 N/A

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

      15. distribute-rgt-out-- N/A

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

      16. *-lft-identity N/A

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

      17. unpow2 N/A

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

      18. lower--.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 93.4

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

   5. Simplified 93.4%

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

   6. Taylor expanded in m around 0

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

      1. lower-/.f64 88.8

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

   8. Simplified 88.8%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \cdot \left(-1 + \frac{m \cdot \left(1 - m\right)}{v}\right) \leq -5 \cdot 10^{+33}:\\ \;\;\;\;-m \cdot \frac{m}{v}\\ \mathbf{elif}\;m \cdot \left(-1 + \frac{m \cdot \left(1 - m\right)}{v}\right) \leq -1 \cdot 10^{-308}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := m \cdot \frac{m}{v}\\ \mathbf{if}\;m \cdot \left(-1 + \frac{m \cdot \left(1 - m\right)}{v}\right) \leq -5 \cdot 10^{+33}:\\ \;\;\;\;-m \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0 - m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (let* ((t_0 (* m (/ m v))))
   (if (<= (* m (+ -1.0 (/ (* m (- 1.0 m)) v))) -5e+33)
     (- (* m t_0))
     (- t_0 m))))

C

double code(double m, double v) {
	double t_0 = m * (m / v);
	double tmp;
	if ((m * (-1.0 + ((m * (1.0 - m)) / v))) <= -5e+33) {
		tmp = -(m * t_0);
	} else {
		tmp = t_0 - m;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: t_0
    real(8) :: tmp
    t_0 = m * (m / v)
    if ((m * ((-1.0d0) + ((m * (1.0d0 - m)) / v))) <= (-5d+33)) then
        tmp = -(m * t_0)
    else
        tmp = t_0 - m
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double t_0 = m * (m / v);
	double tmp;
	if ((m * (-1.0 + ((m * (1.0 - m)) / v))) <= -5e+33) {
		tmp = -(m * t_0);
	} else {
		tmp = t_0 - m;
	}
	return tmp;
}

Python

def code(m, v):
	t_0 = m * (m / v)
	tmp = 0
	if (m * (-1.0 + ((m * (1.0 - m)) / v))) <= -5e+33:
		tmp = -(m * t_0)
	else:
		tmp = t_0 - m
	return tmp

Julia

function code(m, v)
	t_0 = Float64(m * Float64(m / v))
	tmp = 0.0
	if (Float64(m * Float64(-1.0 + Float64(Float64(m * Float64(1.0 - m)) / v))) <= -5e+33)
		tmp = Float64(-Float64(m * t_0));
	else
		tmp = Float64(t_0 - m);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	t_0 = m * (m / v);
	tmp = 0.0;
	if ((m * (-1.0 + ((m * (1.0 - m)) / v))) <= -5e+33)
		tmp = -(m * t_0);
	else
		tmp = t_0 - m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := Block[{t$95$0 = N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(m * N[(-1.0 + N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e+33], (-N[(m * t$95$0), $MachinePrecision]), N[(t$95$0 - m), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m) < -4.99999999999999973e33

   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

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. unpow2 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 98.0

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

   5. Simplified 98.0%

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

      1. lift-neg.f64 N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 98.1

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

   7. Applied egg-rr 98.1%

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

   if -4.99999999999999973e33 < (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m)

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0

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

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

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

      2. associate-/l* N/A

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

      3. unpow2 N/A

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

      4. *-rgt-identity N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 82.1

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

   5. Simplified 82.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 96.6

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

   7. Applied egg-rr 96.6%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \cdot \left(-1 + \frac{m \cdot \left(1 - m\right)}{v}\right) \leq -5 \cdot 10^{+33}:\\ \;\;\;\;-m \cdot \left(m \cdot \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := m \cdot \frac{m}{v}\\ \mathbf{if}\;m \cdot \left(-1 + \frac{m \cdot \left(1 - m\right)}{v}\right) \leq -5 \cdot 10^{+33}:\\ \;\;\;\;-t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0 - m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (let* ((t_0 (* m (/ m v))))
   (if (<= (* m (+ -1.0 (/ (* m (- 1.0 m)) v))) -5e+33) (- t_0) (- t_0 m))))

C

double code(double m, double v) {
	double t_0 = m * (m / v);
	double tmp;
	if ((m * (-1.0 + ((m * (1.0 - m)) / v))) <= -5e+33) {
		tmp = -t_0;
	} else {
		tmp = t_0 - m;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: t_0
    real(8) :: tmp
    t_0 = m * (m / v)
    if ((m * ((-1.0d0) + ((m * (1.0d0 - m)) / v))) <= (-5d+33)) then
        tmp = -t_0
    else
        tmp = t_0 - m
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double t_0 = m * (m / v);
	double tmp;
	if ((m * (-1.0 + ((m * (1.0 - m)) / v))) <= -5e+33) {
		tmp = -t_0;
	} else {
		tmp = t_0 - m;
	}
	return tmp;
}

Python

def code(m, v):
	t_0 = m * (m / v)
	tmp = 0
	if (m * (-1.0 + ((m * (1.0 - m)) / v))) <= -5e+33:
		tmp = -t_0
	else:
		tmp = t_0 - m
	return tmp

Julia

function code(m, v)
	t_0 = Float64(m * Float64(m / v))
	tmp = 0.0
	if (Float64(m * Float64(-1.0 + Float64(Float64(m * Float64(1.0 - m)) / v))) <= -5e+33)
		tmp = Float64(-t_0);
	else
		tmp = Float64(t_0 - m);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	t_0 = m * (m / v);
	tmp = 0.0;
	if ((m * (-1.0 + ((m * (1.0 - m)) / v))) <= -5e+33)
		tmp = -t_0;
	else
		tmp = t_0 - m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := Block[{t$95$0 = N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(m * N[(-1.0 + N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e+33], (-t$95$0), N[(t$95$0 - m), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m) < -4.99999999999999973e33

   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

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

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

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

      2. unpow2 N/A

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

      3. associate-*l* N/A

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

      4. associate-/r* N/A

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

      5. associate-*r/ N/A

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

      6. rgt-mult-inverse N/A

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

      7. unpow2 N/A

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

      8. associate-*r* N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

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

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

      12. div-sub N/A

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

      13. associate-/l* N/A

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

      14. lower-/.f64 N/A

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

      15. distribute-rgt-out-- N/A

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

      16. *-lft-identity N/A

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

      17. unpow2 N/A

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

      18. lower--.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 99.9

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

   5. Simplified 99.9%

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

   6. Taylor expanded in m around 0

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

      1. lower-/.f64 0.1

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

   8. Simplified 0.1%

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

   10. Applied egg-rr 82.1%

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

   if -4.99999999999999973e33 < (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m)

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0

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

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

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

      2. associate-/l* N/A

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

      3. unpow2 N/A

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

      4. *-rgt-identity N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 82.1

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

   5. Simplified 82.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 96.6

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

   7. Applied egg-rr 96.6%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \cdot \left(-1 + \frac{m \cdot \left(1 - m\right)}{v}\right) \leq -5 \cdot 10^{+33}:\\ \;\;\;\;-m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \cdot \left(-1 + \frac{m \cdot \left(1 - m\right)}{v}\right) \leq -5 \cdot 10^{+33}:\\ \;\;\;\;-m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= (* m (+ -1.0 (/ (* m (- 1.0 m)) v))) -5e+33)
   (- (* m (/ m v)))
   (* m (+ (/ m v) -1.0))))

C

double code(double m, double v) {
	double tmp;
	if ((m * (-1.0 + ((m * (1.0 - m)) / v))) <= -5e+33) {
		tmp = -(m * (m / v));
	} else {
		tmp = m * ((m / v) + -1.0);
	}
	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) + ((m * (1.0d0 - m)) / v))) <= (-5d+33)) then
        tmp = -(m * (m / v))
    else
        tmp = m * ((m / v) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if ((m * (-1.0 + ((m * (1.0 - m)) / v))) <= -5e+33) {
		tmp = -(m * (m / v));
	} else {
		tmp = m * ((m / v) + -1.0);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (m * (-1.0 + ((m * (1.0 - m)) / v))) <= -5e+33:
		tmp = -(m * (m / v))
	else:
		tmp = m * ((m / v) + -1.0)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (Float64(m * Float64(-1.0 + Float64(Float64(m * Float64(1.0 - m)) / v))) <= -5e+33)
		tmp = Float64(-Float64(m * Float64(m / v)));
	else
		tmp = Float64(m * Float64(Float64(m / v) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if ((m * (-1.0 + ((m * (1.0 - m)) / v))) <= -5e+33)
		tmp = -(m * (m / v));
	else
		tmp = m * ((m / v) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[N[(m * N[(-1.0 + N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e+33], (-N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]), N[(m * N[(N[(m / v), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m) < -4.99999999999999973e33

   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

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

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

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

      2. unpow2 N/A

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

      3. associate-*l* N/A

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

      4. associate-/r* N/A

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

      5. associate-*r/ N/A

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

      6. rgt-mult-inverse N/A

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

      7. unpow2 N/A

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

      8. associate-*r* N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

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

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

      12. div-sub N/A

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

      13. associate-/l* N/A

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

      14. lower-/.f64 N/A

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

      15. distribute-rgt-out-- N/A

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

      16. *-lft-identity N/A

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

      17. unpow2 N/A

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

      18. lower--.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 99.9

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

   5. Simplified 99.9%

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

   6. Taylor expanded in m around 0

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

      1. lower-/.f64 0.1

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

   8. Simplified 0.1%

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

   10. Applied egg-rr 82.1%

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

   if -4.99999999999999973e33 < (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m)

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0

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

      1. lower-/.f64 96.5

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

   5. Simplified 96.5%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \cdot \left(-1 + \frac{m \cdot \left(1 - m\right)}{v}\right) \leq -5 \cdot 10^{+33}:\\ \;\;\;\;-m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \cdot \left(-1 + \frac{m \cdot \left(1 - m\right)}{v}\right) \leq -1 \cdot 10^{-308}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= (* m (+ -1.0 (/ (* m (- 1.0 m)) v))) -1e-308) (- m) (* m (/ m v))))

C

double code(double m, double v) {
	double tmp;
	if ((m * (-1.0 + ((m * (1.0 - m)) / v))) <= -1e-308) {
		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 * ((-1.0d0) + ((m * (1.0d0 - m)) / v))) <= (-1d-308)) 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 * (-1.0 + ((m * (1.0 - m)) / v))) <= -1e-308) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (m * (-1.0 + ((m * (1.0 - m)) / v))) <= -1e-308:
		tmp = -m
	else:
		tmp = m * (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (Float64(m * Float64(-1.0 + Float64(Float64(m * Float64(1.0 - m)) / v))) <= -1e-308)
		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 * (-1.0 + ((m * (1.0 - m)) / v))) <= -1e-308)
		tmp = -m;
	else
		tmp = m * (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[N[(m * N[(-1.0 + N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1e-308], (-m), N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m) < -9.9999999999999991e-309

   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

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

      2. lower-neg.f64 28.8

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

   5. Simplified 28.8%

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

   if -9.9999999999999991e-309 < (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m)

   1. Initial program 99.5%

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

   3. Taylor expanded in m around inf

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

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

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

      2. unpow2 N/A

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

      3. associate-*l* N/A

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

      4. associate-/r* N/A

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

      5. associate-*r/ N/A

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

      6. rgt-mult-inverse N/A

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

      7. unpow2 N/A

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

      8. associate-*r* N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

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

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

      12. div-sub N/A

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

      13. associate-/l* N/A

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

      14. lower-/.f64 N/A

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

      15. distribute-rgt-out-- N/A

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

      16. *-lft-identity N/A

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

      17. unpow2 N/A

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

      18. lower--.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 93.4

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

   5. Simplified 93.4%

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

   6. Taylor expanded in m around 0

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

      1. lower-/.f64 88.8

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

   8. Simplified 88.8%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \cdot \left(-1 + \frac{m \cdot \left(1 - m\right)}{v}\right) \leq -1 \cdot 10^{-308}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 7.2 \cdot 10^{-15}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m - m \cdot m\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 7.2e-15) (- (* m (/ m v)) m) (* (/ m v) (- m (* m m)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 7.2e-15) {
		tmp = (m * (m / v)) - m;
	} else {
		tmp = (m / v) * (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 <= 7.2d-15) then
        tmp = (m * (m / v)) - m
    else
        tmp = (m / v) * (m - (m * m))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 7.2e-15) {
		tmp = (m * (m / v)) - m;
	} else {
		tmp = (m / v) * (m - (m * m));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 7.2e-15:
		tmp = (m * (m / v)) - m
	else:
		tmp = (m / v) * (m - (m * m))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 7.2e-15)
		tmp = Float64(Float64(m * Float64(m / v)) - m);
	else
		tmp = Float64(Float64(m / v) * Float64(m - Float64(m * m)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 7.2e-15)
		tmp = (m * (m / v)) - m;
	else
		tmp = (m / v) * (m - (m * m));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 7.2e-15], N[(N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision], N[(N[(m / v), $MachinePrecision] * N[(m - N[(m * m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 7.2000000000000002e-15

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0

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

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

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

      2. associate-/l* N/A

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

      3. unpow2 N/A

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

      4. *-rgt-identity N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 84.2

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

   5. Simplified 84.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 99.7

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

   7. Applied egg-rr 99.7%

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

   if 7.2000000000000002e-15 < 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

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

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

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

      2. unpow2 N/A

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

      3. associate-*l* N/A

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

      4. associate-/r* N/A

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

      5. associate-*r/ N/A

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

      6. rgt-mult-inverse N/A

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

      7. unpow2 N/A

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

      8. associate-*r* N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

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

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

      12. div-sub N/A

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

      13. associate-/l* N/A

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

      14. lower-/.f64 N/A

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

      15. distribute-rgt-out-- N/A

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

      16. *-lft-identity N/A

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

      17. unpow2 N/A

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

      18. lower--.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 99.4

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

   5. Simplified 99.4%

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

      1. cancel-sign-sub-inv N/A

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

      2. distribute-rgt1-in N/A

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

      3. +-commutative N/A

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

      4. sub-neg N/A

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

      5. lift--.f64 N/A

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

      6. associate-*l/ N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. associate-*l/ N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-rgt1-in N/A

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

      14. cancel-sign-sub-inv N/A

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

      15. lift-*.f64 N/A

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

      16. lift--.f64 N/A

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

      17. clear-num N/A

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

      18. associate-*l/ N/A

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

      19. div-inv N/A

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

      20. *-commutative N/A

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

      21. times-frac N/A

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

   7. Applied egg-rr 99.5%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 7.2 \cdot 10^{-15}:\\ \;\;\;\;m \cdot \frac{m}{v} - m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m - m \cdot m\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. *-commutative N/A

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

   6. lift--.f64 N/A

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

   7. sub-neg N/A

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

   8. distribute-rgt-in N/A

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

   9. metadata-eval N/A

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

   10. neg-mul-1 N/A

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

   11. lift-/.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. *-commutative N/A

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

   14. associate-/l* N/A

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

   15. associate-*l* N/A

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

   16. lower-fma.f64 N/A

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

   17. lower-*.f64 N/A

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

   18. lower-/.f64 N/A

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

   19. lower-neg.f64 99.8

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 9: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[m_, v_] := N[(m * N[(N[(m / v), $MachinePrecision] * N[(1.0 - m), $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. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. sub-neg N/A

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

   5. lift-/.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-/l* N/A

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

   9. *-commutative N/A

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

   10. lower-fma.f64 N/A

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

   11. lower-/.f64 N/A

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

   12. metadata-eval 99.8

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 10: 27.3% accurate, 9.3× 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. 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

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

   2. lower-neg.f64 22.4

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

5. Simplified 22.4%

   \[\leadsto \color{blue}{-m} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024210 
(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))