a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 9.5s

Alternatives: 10

Speedup: N/A×

• 41.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-/l* 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

   1. clear-num 99.8%

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

   2. un-div-inv 99.9%

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

6. Applied egg-rr 99.9%

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

Alternative 2: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 4.6 \cdot 10^{-150}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{-v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 4.6e-150) (- m) (if (<= m 1.0) (* m (/ m v)) (* m (/ m (- v))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 4.6e-150) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m * (m / v);
	} else {
		tmp = m * (m / -v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 4.6d-150) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = m * (m / v)
    else
        tmp = m * (m / -v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 4.6e-150) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m * (m / v);
	} else {
		tmp = m * (m / -v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 4.6e-150:
		tmp = -m
	elif m <= 1.0:
		tmp = m * (m / v)
	else:
		tmp = m * (m / -v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 4.6e-150)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(m * Float64(m / v));
	else
		tmp = Float64(m * Float64(m / Float64(-v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 4.6e-150)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = m * (m / v);
	else
		tmp = m * (m / -v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 4.6e-150], (-m), If[LessEqual[m, 1.0], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], N[(m * N[(m / (-v)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 4.60000000000000006e-150

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 78.8%

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

      1. neg-mul-1 78.8%

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

   7. Simplified 78.8%

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

   if 4.60000000000000006e-150 < m < 1

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-/l* 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in m around 0 98.6%

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

      1. sub-neg 98.6%

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

      2. metadata-eval 98.6%

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

      3. distribute-lft-in 98.6%

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

      4. associate-/l* 98.5%

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

      5. unpow2 98.5%

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

      6. *-commutative 98.5%

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

      7. neg-mul-1 98.5%

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

      8. unsub-neg 98.5%

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

   7. Simplified 98.5%

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

   8. Taylor expanded in m around inf 77.5%

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

      1. unpow2 77.5%

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

      2. add-sqr-sqrt 77.1%

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

      3. times-frac 77.1%

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

   10. Applied egg-rr 77.1%

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

       1. unpow2 77.1%

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

   12. Simplified 77.1%

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

       1. unpow2 77.1%

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

       2. frac-times 77.1%

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

       3. add-sqr-sqrt 77.5%

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

       4. associate-*l/ 77.6%

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

   14. Applied egg-rr 77.6%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 99.9%

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

      2. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in m around 0 0.1%

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

      1. clear-num 0.1%

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

      2. add-sqr-sqrt 0.1%

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

      3. sqrt-unprod 0.1%

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

      4. sqr-neg 0.1%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 81.6%

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

      7. div-inv 81.6%

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

      8. neg-mul-1 81.6%

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

      9. associate-/r* 81.6%

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

      10. metadata-eval 81.6%

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

   9. Applied egg-rr 81.6%

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

       1. associate-*r/ 81.6%

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

       2. associate-*l/ 81.6%

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

       3. *-commutative 81.6%

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

       4. neg-mul-1 81.6%

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

       5. distribute-neg-frac2 81.6%

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

   11. Simplified 81.6%

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

   12. Taylor expanded in m around inf 81.6%

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

       1. neg-mul-1 81.6%

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

       2. distribute-neg-frac 81.6%

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

   14. Simplified 81.6%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 4.6 \cdot 10^{-150}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{-v}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

MATLAB

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in m around 0 99.2%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in m around inf 98.7%

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

      1. associate-*r/ 98.7%

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

      2. mul-1-neg 98.7%

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

   9. Simplified 98.7%

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

4. Final simplification 99.0%

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

Alternative 4: 97.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in m around 0 99.2%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in m around inf 98.7%

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

      1. associate-*r/ 98.7%

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

      2. mul-1-neg 98.7%

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

   9. Simplified 98.7%

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

       1. distribute-frac-neg 98.7%

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

       2. distribute-frac-neg2 98.7%

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

       3. associate-/r/ 98.7%

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

   11. Applied egg-rr 98.7%

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

4. Final simplification 99.0%

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

Alternative 5: 87.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in m around 0 99.2%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 99.9%

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

      2. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in m around 0 0.1%

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

      1. clear-num 0.1%

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

      2. add-sqr-sqrt 0.1%

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

      3. sqrt-unprod 0.1%

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

      4. sqr-neg 0.1%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 81.6%

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

      7. div-inv 81.6%

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

      8. neg-mul-1 81.6%

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

      9. associate-/r* 81.6%

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

      10. metadata-eval 81.6%

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

   9. Applied egg-rr 81.6%

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

       1. associate-*r/ 81.6%

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

       2. associate-*l/ 81.6%

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

       3. *-commutative 81.6%

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

       4. neg-mul-1 81.6%

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

       5. distribute-neg-frac2 81.6%

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

   11. Simplified 81.6%

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

   12. Taylor expanded in v around 0 81.6%

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

       1. distribute-lft-out 81.6%

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

       2. mul-1-neg 81.6%

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

       3. unpow2 81.6%

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

       4. distribute-lft-out 81.6%

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

       5. +-commutative 81.6%

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

   14. Simplified 81.6%

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

4. Final simplification 90.4%

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

Alternative 6: 87.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in m around 0 99.2%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 99.9%

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

      2. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in m around 0 0.1%

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

      1. clear-num 0.1%

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

      2. add-sqr-sqrt 0.1%

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

      3. sqrt-unprod 0.1%

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

      4. sqr-neg 0.1%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 81.6%

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

      7. div-inv 81.6%

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

      8. neg-mul-1 81.6%

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

      9. associate-/r* 81.6%

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

      10. metadata-eval 81.6%

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

   9. Applied egg-rr 81.6%

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

       1. associate-*r/ 81.6%

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

       2. associate-*l/ 81.6%

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

       3. *-commutative 81.6%

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

       4. neg-mul-1 81.6%

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

       5. distribute-neg-frac2 81.6%

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

   11. Simplified 81.6%

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

4. Final simplification 90.4%

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

Alternative 7: 87.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Python

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in m around 0 99.2%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 99.9%

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

      2. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in m around 0 0.1%

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

      1. clear-num 0.1%

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

      2. add-sqr-sqrt 0.1%

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

      3. sqrt-unprod 0.1%

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

      4. sqr-neg 0.1%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 81.6%

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

      7. div-inv 81.6%

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

      8. neg-mul-1 81.6%

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

      9. associate-/r* 81.6%

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

      10. metadata-eval 81.6%

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

   9. Applied egg-rr 81.6%

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

       1. associate-*r/ 81.6%

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

       2. associate-*l/ 81.6%

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

       3. *-commutative 81.6%

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

       4. neg-mul-1 81.6%

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

       5. distribute-neg-frac2 81.6%

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

   11. Simplified 81.6%

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

   12. Taylor expanded in m around inf 81.6%

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

       1. neg-mul-1 81.6%

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

       2. distribute-neg-frac 81.6%

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

   14. Simplified 81.6%

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

4. Final simplification 90.4%

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

Alternative 8: 99.8% accurate, 1.0× speedup

Math

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

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(m * Float64(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[(m * N[(N[(1.0 - m), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-/l* 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 9: 37.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 7.2 \cdot 10^{-150}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= v 7.2e-150) (* m (/ m v)) (- m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 7.2e-150) {
		tmp = m * (m / v);
	} else {
		tmp = -m;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (v <= 7.2d-150) then
        tmp = m * (m / v)
    else
        tmp = -m
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (v <= 7.2e-150) {
		tmp = m * (m / v);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 7.2e-150:
		tmp = m * (m / v)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 7.2e-150)
		tmp = Float64(m * Float64(m / v));
	else
		tmp = Float64(-m);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (v <= 7.2e-150)
		tmp = m * (m / v);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 7.2e-150], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], (-m)]

Derivation

1. Split input into 2 regimes

2. if v < 7.2000000000000004e-150

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in m around 0 51.0%

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

      1. sub-neg 51.0%

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

      2. metadata-eval 51.0%

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

      3. distribute-lft-in 51.0%

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

      4. associate-/l* 42.1%

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

      5. unpow2 42.1%

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

      6. *-commutative 42.1%

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

      7. neg-mul-1 42.1%

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

      8. unsub-neg 42.1%

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

   7. Simplified 42.1%

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

   8. Taylor expanded in m around inf 33.1%

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

      1. unpow2 33.1%

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

      2. add-sqr-sqrt 32.9%

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

      3. times-frac 39.3%

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

   10. Applied egg-rr 39.3%

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

       1. unpow2 39.3%

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

   12. Simplified 39.3%

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

       1. unpow2 39.3%

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

       2. frac-times 32.9%

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

       3. add-sqr-sqrt 33.1%

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

       4. associate-*l/ 39.6%

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

   14. Applied egg-rr 39.6%

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

   if 7.2000000000000004e-150 < v

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 40.9%

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

      1. neg-mul-1 40.9%

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

   7. Simplified 40.9%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq 7.2 \cdot 10^{-150}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 27.7% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	return -m

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-/l* 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in m around 0 26.3%

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

   1. neg-mul-1 26.3%

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

7. Simplified 26.3%

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

Reproduce

herbie shell --seed 2024100 
(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))