a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 5.9s

Alternatives: 12

Speedup: 1.0×

• 41.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-/l* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 97.7% accurate, 0.9× speedup

Math

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

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.0)
   (* m (+ -1.0 (* m (/ 1.0 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 * (1.0 / 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 * (1.0d0 / 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 * (1.0 / 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 * (1.0 / 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 * Float64(1.0 / v))));
	else
		tmp = Float64(m * Float64(-1.0 + Float64(m / Float64(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 * (1.0 / 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 * N[(1.0 / v), $MachinePrecision]), $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. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-/l* 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in m around 0 97.6%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around inf 95.9%

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

      1. associate-*r/ 95.9%

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

      2. neg-mul-1 95.9%

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

   6. Simplified 95.9%

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

4. Final simplification 96.7%

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

Alternative 3: 87.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Wolfram

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

      1. *-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-/l* 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in m around 0 97.6%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around 0 0.1%

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

      1. neg-mul-1 0.1%

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

      2. +-commutative 0.1%

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

      3. unsub-neg 0.1%

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

   6. Simplified 0.1%

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

      1. unpow2 0.1%

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

      2. associate-/l* 0.1%

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

      3. frac-2neg 0.1%

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

      4. associate-/r/ 0.1%

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

      5. remove-double-neg 0.1%

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

      6. frac-2neg 0.1%

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

      7. neg-mul-1 0.1%

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

      8. *-commutative 0.1%

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

      9. associate-*l* 0.1%

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

      10. *-commutative 0.1%

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

      11. associate-*l* 0.1%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 80.3%

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

      14. distribute-frac-neg 80.3%

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

      15. distribute-frac-neg 80.3%

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

      16. sqr-neg 80.3%

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

      17. sqrt-unprod 73.1%

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

      18. add-sqr-sqrt 73.1%

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

   8. Applied egg-rr 73.1%

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

      1. *-commutative 73.1%

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

      2. associate-*l/ 73.1%

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

      3. associate-*l/ 73.1%

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

      4. *-commutative 73.1%

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

      5. neg-mul-1 73.1%

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

   10. Applied egg-rr 73.1%

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

4. Final simplification 85.4%

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

Alternative 4: 87.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

      1. *-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-/l* 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in m around 0 97.6%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in m around 0 0.1%

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

      1. add-sqr-sqrt 0.1%

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

      2. sqrt-unprod 0.1%

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

      3. *-un-lft-identity 0.1%

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

      4. metadata-eval 0.1%

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

      5. swap-sqr 0.1%

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

      6. *-commutative 0.1%

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

      7. associate-*l/ 0.1%

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

      8. *-un-lft-identity 0.1%

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

      9. *-commutative 0.1%

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

      10. associate-*l/ 0.1%

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

      11. *-un-lft-identity 0.1%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 73.1%

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

      14. clear-num 73.1%

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

      15. associate-*l/ 73.1%

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

      16. metadata-eval 73.1%

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

   8. Applied egg-rr 73.1%

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

4. Final simplification 85.4%

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

Alternative 5: 97.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.0) (* m (+ -1.0 (* m (/ 1.0 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 * (1.0 / 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 * (1.0d0 / 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 * (1.0 / 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 * (1.0 / 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 * Float64(1.0 / 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 * (1.0 / 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 * N[(1.0 / v), $MachinePrecision]), $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. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-/l* 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in m around 0 97.6%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in m around inf 95.8%

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

      1. neg-mul-1 95.8%

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

      2. distribute-neg-frac 95.8%

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

   8. Simplified 95.8%

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

4. Final simplification 96.7%

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

Alternative 6: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-*l/ 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 7: 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 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-/l* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

   1. clear-num 99.8%

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

   2. associate-/r/ 99.8%

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

   3. clear-num 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 8: 74.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.1 \cdot 10^{-151}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{-m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.1e-151) (- m) (if (<= m 1.0) (* m (/ m v)) (* m (/ (- m) v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.1e-151) {
		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 <= 2.1d-151) 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 <= 2.1e-151) {
		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 <= 2.1e-151:
		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 <= 2.1e-151)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(m * Float64(m / v));
	else
		tmp = Float64(m * Float64(Float64(-m) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.1e-151)
		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, 2.1e-151], (-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 < 2.0999999999999999e-151

   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/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 85.5%

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

      1. neg-mul-1 85.5%

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

   6. Simplified 85.5%

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

   if 2.0999999999999999e-151 < m < 1

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l/ 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in v around 0 81.8%

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

   5. Taylor expanded in m around 0 77.3%

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

      1. unpow2 77.3%

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

      2. associate-/l* 77.2%

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

      3. associate-/r/ 77.2%

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

   7. Applied egg-rr 77.2%

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

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in v around 0 99.9%

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

   5. Taylor expanded in m around 0 0.1%

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

      1. unpow2 0.1%

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

      2. associate-/l* 0.1%

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

      3. frac-2neg 0.1%

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

      4. associate-/r/ 0.1%

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

      5. remove-double-neg 0.1%

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

      6. frac-2neg 0.1%

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

      7. neg-mul-1 0.1%

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

      8. *-commutative 0.1%

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

      9. associate-*l* 0.1%

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

      10. *-commutative 0.1%

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

      11. associate-*l* 0.1%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 80.3%

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

      14. distribute-frac-neg 80.3%

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

      15. distribute-frac-neg 80.3%

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

      16. sqr-neg 80.3%

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

      17. sqrt-unprod 73.1%

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

      18. add-sqr-sqrt 73.1%

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

   7. Applied egg-rr 73.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.1 \cdot 10^{-151}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{-m}{v}\\ \end{array} \]

Alternative 9: 87.5% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.0) (* m (+ -1.0 (/ m v))) (- (- m) (/ (* 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 * 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 * 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 * 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 * 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(Float64(-m) - Float64(Float64(m * 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 - ((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[(N[(m * m), $MachinePrecision] / 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. Taylor expanded in m around 0 97.6%

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

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around 0 0.1%

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

      1. neg-mul-1 0.1%

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

      2. +-commutative 0.1%

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

      3. unsub-neg 0.1%

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

   6. Simplified 0.1%

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

      1. unpow2 0.1%

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

      2. associate-/l* 0.1%

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

      3. frac-2neg 0.1%

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

      4. associate-/r/ 0.1%

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

      5. remove-double-neg 0.1%

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

      6. frac-2neg 0.1%

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

      7. neg-mul-1 0.1%

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

      8. *-commutative 0.1%

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

      9. associate-*l* 0.1%

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

      10. *-commutative 0.1%

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

      11. associate-*l* 0.1%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 80.3%

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

      14. distribute-frac-neg 80.3%

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

      15. distribute-frac-neg 80.3%

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

      16. sqr-neg 80.3%

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

      17. sqrt-unprod 73.1%

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

      18. add-sqr-sqrt 73.1%

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

   8. Applied egg-rr 73.1%

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

      1. *-commutative 73.1%

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

      2. associate-*l/ 73.1%

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

      3. associate-*l/ 73.1%

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

      4. *-commutative 73.1%

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

      5. neg-mul-1 73.1%

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

   10. Applied egg-rr 73.1%

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

4. Final simplification 85.4%

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

Alternative 10: 38.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 7.5 \cdot 10^{-152} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (or (<= m 7.5e-152) (not (<= m 1.0))) (- m) (* m (/ m v))))

C

double code(double m, double v) {
	double tmp;
	if ((m <= 7.5e-152) || !(m <= 1.0)) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if ((m <= 7.5d-152) .or. (.not. (m <= 1.0d0))) then
        tmp = -m
    else
        tmp = m * (m / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if ((m <= 7.5e-152) || !(m <= 1.0)) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (m <= 7.5e-152) or not (m <= 1.0):
		tmp = -m
	else:
		tmp = m * (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if ((m <= 7.5e-152) || !(m <= 1.0))
		tmp = Float64(-m);
	else
		tmp = Float64(m * Float64(m / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if ((m <= 7.5e-152) || ~((m <= 1.0)))
		tmp = -m;
	else
		tmp = m * (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[Or[LessEqual[m, 7.5e-152], N[Not[LessEqual[m, 1.0]], $MachinePrecision]], (-m), N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 7.5e-152 or 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around 0 32.9%

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

      1. neg-mul-1 32.9%

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

   6. Simplified 32.9%

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

   if 7.5e-152 < m < 1

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l/ 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in v around 0 81.8%

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

   5. Taylor expanded in m around 0 77.3%

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

      1. unpow2 77.3%

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

      2. associate-/l* 77.2%

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

      3. associate-/r/ 77.2%

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

   7. Applied egg-rr 77.2%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 7.5 \cdot 10^{-152} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]

Alternative 11: 87.5% accurate, 1.2× 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(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 * (-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. Taylor expanded in m around 0 97.6%

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

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in v around 0 99.9%

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

   5. Taylor expanded in m around 0 0.1%

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

      1. unpow2 0.1%

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

      2. associate-/l* 0.1%

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

      3. frac-2neg 0.1%

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

      4. associate-/r/ 0.1%

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

      5. remove-double-neg 0.1%

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

      6. frac-2neg 0.1%

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

      7. neg-mul-1 0.1%

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

      8. *-commutative 0.1%

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

      9. associate-*l* 0.1%

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

      10. *-commutative 0.1%

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

      11. associate-*l* 0.1%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 80.3%

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

      14. distribute-frac-neg 80.3%

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

      15. distribute-frac-neg 80.3%

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

      16. sqr-neg 80.3%

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

      17. sqrt-unprod 73.1%

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

      18. add-sqr-sqrt 73.1%

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

   7. Applied egg-rr 73.1%

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

4. Final simplification 85.4%

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

Alternative 12: 28.2% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	return -m

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-*l/ 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in m around 0 29.0%

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

   1. neg-mul-1 29.0%

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

6. Simplified 29.0%

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

7. Final simplification 29.0%

   \[\leadsto -m \]

Reproduce

herbie shell --seed 2023322 
(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))