a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 9.9s

Alternatives: 11

Speedup: 1.0×

• 42.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \left(0 - m\right) - \frac{m}{\frac{v}{m \cdot \left(m + -1\right)}} \end{array} \]

FPCore

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

C

double code(double m, double v) {
	return (0.0 - m) - (m / (v / (m * (m + -1.0))));
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    code = (0.0d0 - m) - (m / (v / (m * (m + (-1.0d0)))))
end function

Java

public static double code(double m, double v) {
	return (0.0 - m) - (m / (v / (m * (m + -1.0))));
}

Python

def code(m, v):
	return (0.0 - m) - (m / (v / (m * (m + -1.0))))

Julia

function code(m, v)
	return Float64(Float64(0.0 - m) - Float64(m / Float64(v / Float64(m * Float64(m + -1.0)))))
end

MATLAB

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

Wolfram

code[m_, v_] := N[(N[(0.0 - m), $MachinePrecision] - N[(m / N[(v / N[(m * N[(m + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. *-commutative N/A

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

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

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

   3. *-rgt-identity N/A

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

   4. fmm-def N/A

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

   5. fma-define N/A

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

   6. frac-2neg N/A

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

   7. distribute-frac-neg N/A

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

   8. distribute-rgt-neg-out N/A

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

   9. distribute-neg-out N/A

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

   10. neg-lowering-neg.f64 N/A

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

   11. +-lowering-+.f64 N/A

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

4. Applied egg-rr 99.9%

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

5. Final simplification 99.9%

   \[\leadsto \left(0 - m\right) - \frac{m}{\frac{v}{m \cdot \left(m + -1\right)}} \]
6. Add Preprocessing

Alternative 2: 99.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 3 \cdot 10^{-30}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 3e-30) (- (/ m (/ v m)) m) (/ m (/ v (* m (- 1.0 m))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 3e-30) {
		tmp = (m / (v / m)) - m;
	} 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 <= 3d-30) then
        tmp = (m / (v / m)) - m
    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 <= 3e-30) {
		tmp = (m / (v / m)) - m;
	} else {
		tmp = m / (v / (m * (1.0 - m)));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 3e-30:
		tmp = (m / (v / m)) - m
	else:
		tmp = m / (v / (m * (1.0 - m)))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 3e-30)
		tmp = Float64(Float64(m / Float64(v / m)) - m);
	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 <= 3e-30)
		tmp = (m / (v / m)) - m;
	else
		tmp = m / (v / (m * (1.0 - m)));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 3e-30], N[(N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision] - m), $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 < 2.9999999999999999e-30

   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

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

      1. /-lowering-/.f64 99.7%

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

   5. Simplified 99.7%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-rgt-in N/A

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

      5. associate-/r/ N/A

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

      6. neg-mul-1 N/A

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

      7. unsub-neg N/A

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

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

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

      9. /-lowering-/.f64 N/A

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

      10. /-lowering-/.f64 99.8%

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

   7. Applied egg-rr 99.8%

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

   if 2.9999999999999999e-30 < 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

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

      3. associate-*l* N/A

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

      4. associate-/r* N/A

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

      5. associate-*r/ N/A

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

      6. rgt-mult-inverse N/A

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

      7. unpow2 N/A

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

      8. associate-*r* N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

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

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

      12. div-sub N/A

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

      13. associate-/l* N/A

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

      14. /-lowering-/.f64 N/A

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

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

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

      16. --lowering--.f64 99.9%

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

   5. Simplified 99.9%

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

      1. associate-/r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. +-commutative N/A

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

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

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

      10. associate-/r/ N/A

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

      11. associate-/r* N/A

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

      12. distribute-neg-frac2 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. associate-/r* N/A

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

      15. distribute-neg-frac2 N/A

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

      16. +-commutative N/A

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

      17. distribute-neg-in N/A

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

      18. metadata-eval N/A

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

      19. sub-neg N/A

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

      20. associate-/r* N/A

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

      21. /-lowering-/.f64 N/A

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

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

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

      23. --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. Add Preprocessing

Alternative 3: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 4.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(m \cdot \frac{1 - m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 4.1e-23) (- (/ m (/ v m)) m) (* m (* m (/ (- 1.0 m) v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 4.1e-23) {
		tmp = (m / (v / m)) - m;
	} else {
		tmp = m * (m * ((1.0 - m) / v));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 4.1d-23) then
        tmp = (m / (v / m)) - m
    else
        tmp = m * (m * ((1.0d0 - m) / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 4.1e-23) {
		tmp = (m / (v / m)) - m;
	} else {
		tmp = m * (m * ((1.0 - m) / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 4.1e-23:
		tmp = (m / (v / m)) - m
	else:
		tmp = m * (m * ((1.0 - m) / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 4.1e-23)
		tmp = Float64(Float64(m / Float64(v / m)) - m);
	else
		tmp = Float64(m * Float64(m * Float64(Float64(1.0 - m) / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 4.1e-23)
		tmp = (m / (v / m)) - m;
	else
		tmp = m * (m * ((1.0 - m) / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 4.1e-23], N[(N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision], N[(m * N[(m * N[(N[(1.0 - m), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 4.10000000000000029e-23

   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

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

      1. /-lowering-/.f64 99.7%

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

   5. Simplified 99.7%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-rgt-in N/A

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

      5. associate-/r/ N/A

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

      6. neg-mul-1 N/A

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

      7. unsub-neg N/A

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

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

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

      9. /-lowering-/.f64 N/A

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

      10. /-lowering-/.f64 99.8%

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

   7. Applied egg-rr 99.8%

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

   if 4.10000000000000029e-23 < 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

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

      3. associate-*l* N/A

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

      4. associate-/r* N/A

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

      5. associate-*r/ N/A

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

      6. rgt-mult-inverse N/A

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

      7. unpow2 N/A

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

      8. associate-*r* N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

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

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

      12. div-sub N/A

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

      13. associate-/l* N/A

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

      14. /-lowering-/.f64 N/A

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

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

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

      16. --lowering--.f64 99.9%

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

   5. Simplified 99.9%

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

      1. associate-*r/ 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 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 4.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(m \cdot \frac{1 - m}{v}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.0d0) then
        tmp = (m / (v / m)) - m
    else
        tmp = (m * (m * m)) / (0.0d0 - v)
    end if
    code = tmp
end function

Java

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

Python

def code(m, v):
	tmp = 0
	if m <= 1.0:
		tmp = (m / (v / m)) - m
	else:
		tmp = (m * (m * m)) / (0.0 - v)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := If[LessEqual[m, 1.0], N[(N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision] - m), $MachinePrecision], N[(N[(m * N[(m * m), $MachinePrecision]), $MachinePrecision] / N[(0.0 - v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. 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 99.3%

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

   5. Simplified 99.3%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-rgt-in N/A

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

      5. associate-/r/ N/A

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

      6. neg-mul-1 N/A

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

      7. unsub-neg N/A

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

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

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

      9. /-lowering-/.f64 N/A

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

      10. /-lowering-/.f64 99.4%

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

   7. Applied egg-rr 99.4%

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

   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. Step-by-step derivation

      1. *-commutative N/A

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

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

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

      3. *-rgt-identity N/A

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

      4. fmm-def N/A

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

      5. fma-define N/A

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

      6. frac-2neg N/A

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

      7. distribute-frac-neg N/A

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

      8. distribute-rgt-neg-out N/A

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

      9. distribute-neg-out N/A

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

      10. neg-lowering-neg.f64 N/A

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

      11. +-lowering-+.f64 N/A

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in m around inf

      \[\leadsto \mathsf{neg.f64}\left(\color{blue}{\left(\frac{{m}^{3}}{v}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left({m}^{3}\right), v\right)\right) \]

      2. cube-mult N/A

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

      3. unpow2 N/A

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 97.5%

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

   7. Simplified 97.5%

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

4. Final simplification 98.5%

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

Alternative 5: 51.1% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0

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

      1. /-lowering-/.f64 99.3%

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

   5. Simplified 99.3%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-rgt-in N/A

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

      5. associate-/r/ N/A

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

      6. neg-mul-1 N/A

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

      7. unsub-neg N/A

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

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

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

      9. /-lowering-/.f64 N/A

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

      10. /-lowering-/.f64 99.4%

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

   7. Applied egg-rr 99.4%

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

   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. remove-double-div N/A

         \[\leadsto \mathsf{neg}\left(\frac{1}{\frac{1}{m}}\right) \]

      3. distribute-frac-neg2 N/A

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

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

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. /-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. Add Preprocessing

Alternative 6: 51.1% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

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

      1. *-commutative N/A

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

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

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

      3. *-lft-identity N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. /-lowering-/.f64 N/A

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

      10. --lowering--.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in m around 0

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

      1. /-lowering-/.f64 99.4%

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

   7. Simplified 99.4%

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

   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. remove-double-div N/A

         \[\leadsto \mathsf{neg}\left(\frac{1}{\frac{1}{m}}\right) \]

      3. distribute-frac-neg2 N/A

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

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

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. /-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. Add Preprocessing

Alternative 7: 51.1% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Python

def code(m, v):
	tmp = 0
	if m <= 1.0:
		tmp = m * (-1.0 + (m / v))
	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(-1.0 + Float64(m / v)));
	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 * (-1.0 + (m / v));
	else
		tmp = 1.0 / (-1.0 / m);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.7%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. 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 99.3%

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

   5. Simplified 99.3%

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

   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. remove-double-div N/A

         \[\leadsto \mathsf{neg}\left(\frac{1}{\frac{1}{m}}\right) \]

      3. distribute-frac-neg2 N/A

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

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

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. /-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 56.2%

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

Alternative 8: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 9: 37.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 1.02 \cdot 10^{-164}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;0 - m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= v 1.02e-164) (/ m (/ v m)) (- 0.0 m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 1.02e-164) {
		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 <= 1.02d-164) 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 <= 1.02e-164) {
		tmp = m / (v / m);
	} else {
		tmp = 0.0 - m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 1.02e-164:
		tmp = m / (v / m)
	else:
		tmp = 0.0 - m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 1.02e-164)
		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 <= 1.02e-164)
		tmp = m / (v / m);
	else
		tmp = 0.0 - m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 1.02e-164], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], N[(0.0 - m), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if v < 1.02e-164

   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 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

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

      3. associate-*l* N/A

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

      4. associate-/r* N/A

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

      5. associate-*r/ N/A

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

      6. rgt-mult-inverse N/A

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

      7. unpow2 N/A

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

      8. associate-*r* N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

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

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

      12. div-sub N/A

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

      13. associate-/l* N/A

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

      14. /-lowering-/.f64 N/A

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

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

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

      16. --lowering--.f64 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in m around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({m}^{2}\right), \color{blue}{v}\right) \]

      2. unpow2 N/A

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

      3. *-lowering-*.f64 32.4%

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

   8. Simplified 32.4%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

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

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

      4. /-lowering-/.f64 41.6%

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

   10. Applied egg-rr 41.6%

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

   if 1.02e-164 < 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 45.5%

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

   5. Simplified 45.5%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 45.5%

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

   7. Applied egg-rr 45.5%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq 1.02 \cdot 10^{-164}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;0 - m\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 1.85 \cdot 10^{-164}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;0 - m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= v 1.85e-164) (* m (/ m v)) (- 0.0 m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 1.85e-164) {
		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 <= 1.85d-164) 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 <= 1.85e-164) {
		tmp = m * (m / v);
	} else {
		tmp = 0.0 - m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 1.85e-164:
		tmp = m * (m / v)
	else:
		tmp = 0.0 - m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 1.85e-164)
		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 <= 1.85e-164)
		tmp = m * (m / v);
	else
		tmp = 0.0 - m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 1.85e-164], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], N[(0.0 - m), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if v < 1.85e-164

   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 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

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

      3. associate-*l* N/A

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

      4. associate-/r* N/A

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

      5. associate-*r/ N/A

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

      6. rgt-mult-inverse N/A

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

      7. unpow2 N/A

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

      8. associate-*r* N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

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

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

      12. div-sub N/A

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

      13. associate-/l* N/A

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

      14. /-lowering-/.f64 N/A

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

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

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

      16. --lowering--.f64 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in m around 0

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

      1. /-lowering-/.f64 41.6%

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

   8. Simplified 41.6%

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

   if 1.85e-164 < 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 45.5%

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

   5. Simplified 45.5%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 45.5%

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

   7. Applied egg-rr 45.5%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq 1.85 \cdot 10^{-164}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;0 - m\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 26.9% 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 30.6%

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

5. Simplified 30.6%

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

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 30.6%

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

7. Applied egg-rr 30.6%

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

8. Final simplification 30.6%

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

Reproduce

herbie shell --seed 2024164 
(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))