a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 7.2s

Alternatives: 17

Speedup: 1.0×

• 41.9% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 73.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.4 \cdot 10^{-210}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 8.8 \cdot 10^{-190}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{elif}\;m \leq 2.6 \cdot 10^{-123}:\\ \;\;\;\;\frac{m \cdot \left(-v\right)}{v}\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(-1 - \frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.4e-210)
   (- m)
   (if (<= m 8.8e-190)
     (* m (/ m v))
     (if (<= m 2.6e-123)
       (/ (* m (- v)) v)
       (if (<= m 1.0) (/ m (/ v m)) (* m (- -1.0 (/ m v))))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.4e-210) {
		tmp = -m;
	} else if (m <= 8.8e-190) {
		tmp = m * (m / v);
	} else if (m <= 2.6e-123) {
		tmp = (m * -v) / v;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} 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 <= 2.4d-210) then
        tmp = -m
    else if (m <= 8.8d-190) then
        tmp = m * (m / v)
    else if (m <= 2.6d-123) then
        tmp = (m * -v) / v
    else if (m <= 1.0d0) then
        tmp = m / (v / m)
    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 <= 2.4e-210) {
		tmp = -m;
	} else if (m <= 8.8e-190) {
		tmp = m * (m / v);
	} else if (m <= 2.6e-123) {
		tmp = (m * -v) / v;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = m * (-1.0 - (m / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.4e-210:
		tmp = -m
	elif m <= 8.8e-190:
		tmp = m * (m / v)
	elif m <= 2.6e-123:
		tmp = (m * -v) / v
	elif m <= 1.0:
		tmp = m / (v / m)
	else:
		tmp = m * (-1.0 - (m / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.4e-210)
		tmp = Float64(-m);
	elseif (m <= 8.8e-190)
		tmp = Float64(m * Float64(m / v));
	elseif (m <= 2.6e-123)
		tmp = Float64(Float64(m * Float64(-v)) / v);
	elseif (m <= 1.0)
		tmp = Float64(m / Float64(v / m));
	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 <= 2.4e-210)
		tmp = -m;
	elseif (m <= 8.8e-190)
		tmp = m * (m / v);
	elseif (m <= 2.6e-123)
		tmp = (m * -v) / v;
	elseif (m <= 1.0)
		tmp = m / (v / m);
	else
		tmp = m * (-1.0 - (m / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.4e-210], (-m), If[LessEqual[m, 8.8e-190], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 2.6e-123], N[(N[(m * (-v)), $MachinePrecision] / v), $MachinePrecision], If[LessEqual[m, 1.0], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], N[(m * N[(-1.0 - N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if m < 2.40000000000000004e-210

   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%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in m around 0 88.1%

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

      1. neg-mul-1 88.1%

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

   7. Simplified 88.1%

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

   if 2.40000000000000004e-210 < m < 8.80000000000000017e-190

   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* 99.6%

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

      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 99.6%

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

   6. Taylor expanded in m around inf 4.9%

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

      1. unpow2 29.8%

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

      2. associate-*l/ 100.0%

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

   8. Applied egg-rr 67.5%

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

   if 8.80000000000000017e-190 < m < 2.59999999999999995e-123

   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* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in m around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. distribute-lft-in 99.9%

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

      4. *-commutative 99.9%

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

      5. neg-mul-1 99.9%

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

      6. unsub-neg 99.9%

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

      7. associate-/l* 96.2%

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

      8. unpow2 96.2%

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

   7. Simplified 96.2%

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

      1. unpow2 96.2%

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

      2. associate-*l/ 99.9%

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

   9. Applied egg-rr 99.9%

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

   10. Taylor expanded in v around 0 96.2%

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

       1. associate-*r* 96.2%

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

       2. neg-mul-1 96.2%

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

       3. unpow2 96.2%

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

       4. sqr-neg 96.2%

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

       5. distribute-lft-out 96.2%

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

       6. unsub-neg 96.2%

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

   12. Simplified 96.2%

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

   13. Taylor expanded in m around 0 85.2%

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

       1. associate-*r* 85.2%

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

       2. mul-1-neg 85.2%

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

   15. Simplified 85.2%

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

   if 2.59999999999999995e-123 < 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* 99.4%

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

      4. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in m around 0 96.2%

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

   6. Taylor expanded in m around inf 77.0%

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

      1. unpow2 96.5%

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

      2. associate-*l/ 96.5%

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

   8. Applied egg-rr 77.0%

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

      1. *-commutative 96.5%

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

      2. clear-num 96.2%

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

      3. un-div-inv 96.6%

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

   10. Applied egg-rr 77.1%

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

   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. Taylor expanded in m around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. neg-mul-1 0.1%

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

      6. unsub-neg 0.1%

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

      7. associate-/l* 0.1%

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

      8. unpow2 0.1%

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

   7. Simplified 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*l/ 0.1%

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

   9. Applied egg-rr 0.1%

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

       1. frac-2neg 0.1%

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

       2. associate-*l/ 0.1%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 72.3%

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

       5. sqr-neg 72.3%

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

       6. sqrt-unprod 68.1%

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

       7. add-sqr-sqrt 68.1%

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

   11. Applied egg-rr 68.1%

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

   12. Taylor expanded in m around 0 68.1%

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

       1. sub-neg 68.1%

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

       2. metadata-eval 68.1%

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

       3. +-commutative 68.1%

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

       4. mul-1-neg 68.1%

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

       5. unsub-neg 68.1%

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

   14. Simplified 68.1%

       \[\leadsto \color{blue}{m \cdot \left(-1 - \frac{m}{v}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.4 \cdot 10^{-210}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 8.8 \cdot 10^{-190}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{elif}\;m \leq 2.6 \cdot 10^{-123}:\\ \;\;\;\;\frac{m \cdot \left(-v\right)}{v}\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(-1 - \frac{m}{v}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.5 \cdot 10^{-210}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1.02 \cdot 10^{-190}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{elif}\;m \leq 4.2 \cdot 10^{-123}:\\ \;\;\;\;\frac{m \cdot \left(-v\right)}{v}\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-m \cdot m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.5e-210)
   (- m)
   (if (<= m 1.02e-190)
     (* m (/ m v))
     (if (<= m 4.2e-123)
       (/ (* m (- v)) v)
       (if (<= m 1.0) (/ m (/ v m)) (/ (- (* m m)) v))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.5e-210) {
		tmp = -m;
	} else if (m <= 1.02e-190) {
		tmp = m * (m / v);
	} else if (m <= 4.2e-123) {
		tmp = (m * -v) / v;
	} else if (m <= 1.0) {
		tmp = m / (v / 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 <= 2.5d-210) then
        tmp = -m
    else if (m <= 1.02d-190) then
        tmp = m * (m / v)
    else if (m <= 4.2d-123) then
        tmp = (m * -v) / v
    else if (m <= 1.0d0) then
        tmp = m / (v / 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 <= 2.5e-210) {
		tmp = -m;
	} else if (m <= 1.02e-190) {
		tmp = m * (m / v);
	} else if (m <= 4.2e-123) {
		tmp = (m * -v) / v;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = -(m * m) / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.5e-210:
		tmp = -m
	elif m <= 1.02e-190:
		tmp = m * (m / v)
	elif m <= 4.2e-123:
		tmp = (m * -v) / v
	elif m <= 1.0:
		tmp = m / (v / m)
	else:
		tmp = -(m * m) / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.5e-210)
		tmp = Float64(-m);
	elseif (m <= 1.02e-190)
		tmp = Float64(m * Float64(m / v));
	elseif (m <= 4.2e-123)
		tmp = Float64(Float64(m * Float64(-v)) / v);
	elseif (m <= 1.0)
		tmp = Float64(m / Float64(v / m));
	else
		tmp = Float64(Float64(-Float64(m * m)) / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.5e-210)
		tmp = -m;
	elseif (m <= 1.02e-190)
		tmp = m * (m / v);
	elseif (m <= 4.2e-123)
		tmp = (m * -v) / v;
	elseif (m <= 1.0)
		tmp = m / (v / m);
	else
		tmp = -(m * m) / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.5e-210], (-m), If[LessEqual[m, 1.02e-190], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 4.2e-123], N[(N[(m * (-v)), $MachinePrecision] / v), $MachinePrecision], If[LessEqual[m, 1.0], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], N[((-N[(m * m), $MachinePrecision]) / v), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if m < 2.5000000000000001e-210

   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%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in m around 0 88.1%

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

      1. neg-mul-1 88.1%

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

   7. Simplified 88.1%

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

   if 2.5000000000000001e-210 < m < 1.02e-190

   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* 99.6%

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

      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 99.6%

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

   6. Taylor expanded in m around inf 4.9%

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

      1. unpow2 29.8%

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

      2. associate-*l/ 100.0%

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

   8. Applied egg-rr 67.5%

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

   if 1.02e-190 < m < 4.1999999999999998e-123

   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* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in m around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. distribute-lft-in 99.9%

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

      4. *-commutative 99.9%

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

      5. neg-mul-1 99.9%

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

      6. unsub-neg 99.9%

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

      7. associate-/l* 96.2%

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

      8. unpow2 96.2%

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

   7. Simplified 96.2%

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

      1. unpow2 96.2%

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

      2. associate-*l/ 99.9%

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

   9. Applied egg-rr 99.9%

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

   10. Taylor expanded in v around 0 96.2%

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

       1. associate-*r* 96.2%

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

       2. neg-mul-1 96.2%

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

       3. unpow2 96.2%

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

       4. sqr-neg 96.2%

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

       5. distribute-lft-out 96.2%

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

       6. unsub-neg 96.2%

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

   12. Simplified 96.2%

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

   13. Taylor expanded in m around 0 85.2%

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

       1. associate-*r* 85.2%

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

       2. mul-1-neg 85.2%

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

   15. Simplified 85.2%

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

   if 4.1999999999999998e-123 < 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* 99.4%

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

      4. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in m around 0 96.2%

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

   6. Taylor expanded in m around inf 77.0%

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

      1. unpow2 96.5%

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

      2. associate-*l/ 96.5%

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

   8. Applied egg-rr 77.0%

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

      1. *-commutative 96.5%

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

      2. clear-num 96.2%

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

      3. un-div-inv 96.6%

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

   10. Applied egg-rr 77.1%

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

   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. Taylor expanded in m around 0 0.1%

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

   6. Taylor expanded in m around inf 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*l/ 0.1%

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

   8. Applied egg-rr 0.1%

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

      1. frac-2neg 0.1%

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

      2. associate-*l/ 0.1%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 72.3%

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

      5. sqr-neg 72.3%

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

      6. sqrt-unprod 68.1%

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

      7. add-sqr-sqrt 68.1%

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

   10. Applied egg-rr 68.1%

       \[\leadsto \color{blue}{\frac{\left(-m\right) \cdot m}{v}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.5 \cdot 10^{-210}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1.02 \cdot 10^{-190}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{elif}\;m \leq 4.2 \cdot 10^{-123}:\\ \;\;\;\;\frac{m \cdot \left(-v\right)}{v}\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-m \cdot m}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.45 \cdot 10^{-210}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1.22 \cdot 10^{-191}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{elif}\;m \leq 5.3 \cdot 10^{-123}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-m \cdot m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.45e-210)
   (- m)
   (if (<= m 1.22e-191)
     (* m (/ m v))
     (if (<= m 5.3e-123)
       (- m)
       (if (<= m 1.0) (/ m (/ v m)) (/ (- (* m m)) v))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.45e-210) {
		tmp = -m;
	} else if (m <= 1.22e-191) {
		tmp = m * (m / v);
	} else if (m <= 5.3e-123) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / 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 <= 2.45d-210) then
        tmp = -m
    else if (m <= 1.22d-191) then
        tmp = m * (m / v)
    else if (m <= 5.3d-123) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = m / (v / 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 <= 2.45e-210) {
		tmp = -m;
	} else if (m <= 1.22e-191) {
		tmp = m * (m / v);
	} else if (m <= 5.3e-123) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = -(m * m) / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.45e-210:
		tmp = -m
	elif m <= 1.22e-191:
		tmp = m * (m / v)
	elif m <= 5.3e-123:
		tmp = -m
	elif m <= 1.0:
		tmp = m / (v / m)
	else:
		tmp = -(m * m) / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.45e-210)
		tmp = Float64(-m);
	elseif (m <= 1.22e-191)
		tmp = Float64(m * Float64(m / v));
	elseif (m <= 5.3e-123)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(m / Float64(v / m));
	else
		tmp = Float64(Float64(-Float64(m * m)) / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.45e-210)
		tmp = -m;
	elseif (m <= 1.22e-191)
		tmp = m * (m / v);
	elseif (m <= 5.3e-123)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = m / (v / m);
	else
		tmp = -(m * m) / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.45e-210], (-m), If[LessEqual[m, 1.22e-191], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 5.3e-123], (-m), If[LessEqual[m, 1.0], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], N[((-N[(m * m), $MachinePrecision]) / v), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if m < 2.4499999999999999e-210 or 1.22e-191 < m < 5.29999999999999971e-123

   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%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in m around 0 87.0%

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

      1. neg-mul-1 87.0%

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

   7. Simplified 87.0%

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

   if 2.4499999999999999e-210 < m < 1.22e-191

   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* 99.6%

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

      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 99.6%

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

   6. Taylor expanded in m around inf 4.9%

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

      1. unpow2 29.8%

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

      2. associate-*l/ 100.0%

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

   8. Applied egg-rr 67.5%

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

   if 5.29999999999999971e-123 < 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* 99.4%

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

      4. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in m around 0 96.2%

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

   6. Taylor expanded in m around inf 77.0%

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

      1. unpow2 96.5%

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

      2. associate-*l/ 96.5%

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

   8. Applied egg-rr 77.0%

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

      1. *-commutative 96.5%

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

      2. clear-num 96.2%

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

      3. un-div-inv 96.6%

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

   10. Applied egg-rr 77.1%

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

   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. Taylor expanded in m around 0 0.1%

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

   6. Taylor expanded in m around inf 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*l/ 0.1%

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

   8. Applied egg-rr 0.1%

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

      1. frac-2neg 0.1%

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

      2. associate-*l/ 0.1%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 72.3%

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

      5. sqr-neg 72.3%

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

      6. sqrt-unprod 68.1%

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

      7. add-sqr-sqrt 68.1%

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

   10. Applied egg-rr 68.1%

       \[\leadsto \color{blue}{\frac{\left(-m\right) \cdot m}{v}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.45 \cdot 10^{-210}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1.22 \cdot 10^{-191}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{elif}\;m \leq 5.3 \cdot 10^{-123}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-m \cdot m}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.5 \cdot 10^{-210}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1.22 \cdot 10^{-191}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{elif}\;m \leq 1.1 \cdot 10^{-122}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{-m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.5e-210)
   (- m)
   (if (<= m 1.22e-191)
     (* m (/ m v))
     (if (<= m 1.1e-122)
       (- m)
       (if (<= m 1.0) (/ m (/ v m)) (/ m (/ v (- m))))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.5e-210) {
		tmp = -m;
	} else if (m <= 1.22e-191) {
		tmp = m * (m / v);
	} else if (m <= 1.1e-122) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = 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 <= 2.5d-210) then
        tmp = -m
    else if (m <= 1.22d-191) then
        tmp = m * (m / v)
    else if (m <= 1.1d-122) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = m / (v / m)
    else
        tmp = m / (v / -m)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 2.5e-210) {
		tmp = -m;
	} else if (m <= 1.22e-191) {
		tmp = m * (m / v);
	} else if (m <= 1.1e-122) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = m / (v / -m);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.5e-210:
		tmp = -m
	elif m <= 1.22e-191:
		tmp = m * (m / v)
	elif m <= 1.1e-122:
		tmp = -m
	elif m <= 1.0:
		tmp = m / (v / m)
	else:
		tmp = m / (v / -m)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.5e-210)
		tmp = Float64(-m);
	elseif (m <= 1.22e-191)
		tmp = Float64(m * Float64(m / v));
	elseif (m <= 1.1e-122)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(m / Float64(v / m));
	else
		tmp = Float64(m / Float64(v / Float64(-m)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.5e-210)
		tmp = -m;
	elseif (m <= 1.22e-191)
		tmp = m * (m / v);
	elseif (m <= 1.1e-122)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = m / (v / m);
	else
		tmp = m / (v / -m);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.5e-210], (-m), If[LessEqual[m, 1.22e-191], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 1.1e-122], (-m), If[LessEqual[m, 1.0], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], N[(m / N[(v / (-m)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if m < 2.5000000000000001e-210 or 1.22e-191 < m < 1.1e-122

   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%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in m around 0 87.0%

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

      1. neg-mul-1 87.0%

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

   7. Simplified 87.0%

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

   if 2.5000000000000001e-210 < m < 1.22e-191

   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* 99.6%

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

      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 99.6%

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

   6. Taylor expanded in m around inf 4.9%

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

      1. unpow2 29.8%

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

      2. associate-*l/ 100.0%

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

   8. Applied egg-rr 67.5%

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

   if 1.1e-122 < 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* 99.4%

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

      4. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in m around 0 96.2%

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

   6. Taylor expanded in m around inf 77.0%

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

      1. unpow2 96.5%

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

      2. associate-*l/ 96.5%

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

   8. Applied egg-rr 77.0%

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

      1. *-commutative 96.5%

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

      2. clear-num 96.2%

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

      3. un-div-inv 96.6%

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

   10. Applied egg-rr 77.1%

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

   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. Taylor expanded in m around 0 0.1%

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

   6. Taylor expanded in m around inf 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*l/ 0.1%

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

   8. Applied egg-rr 0.1%

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

      1. add-sqr-sqrt 0.1%

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

      2. sqrt-unprod 0.1%

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

      3. sqr-neg 0.1%

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

      4. distribute-frac-neg2 0.1%

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

      5. distribute-frac-neg2 0.1%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 68.1%

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

      8. associate-/r/ 68.1%

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

      9. frac-2neg 68.1%

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

      10. distribute-frac-neg 68.1%

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

      11. remove-double-neg 68.1%

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

   10. Applied egg-rr 68.1%

       \[\leadsto \color{blue}{\frac{-m}{\frac{v}{m}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.5 \cdot 10^{-210}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1.22 \cdot 10^{-191}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{elif}\;m \leq 1.1 \cdot 10^{-122}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{-m}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

      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 98.8%

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

      1. sub-neg 98.8%

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

      2. metadata-eval 98.8%

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

      3. distribute-lft-in 98.8%

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

      4. *-commutative 98.8%

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

      5. neg-mul-1 98.8%

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

      6. unsub-neg 98.8%

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

      7. associate-/l* 87.5%

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

      8. unpow2 87.5%

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

   7. Simplified 87.5%

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

      1. unpow2 87.5%

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

      2. associate-*l/ 98.8%

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

   9. Applied egg-rr 98.8%

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

       1. *-commutative 98.8%

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

       2. clear-num 98.7%

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

       3. un-div-inv 98.9%

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

   11. Applied egg-rr 98.9%

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

   if 1 < m

   1. Initial program 99.9%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. 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 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. Taylor expanded in m around inf 98.4%

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

      1. associate-*r/ 98.4%

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

      2. neg-mul-1 98.4%

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

   9. Simplified 98.4%

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

4. Final simplification 98.6%

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

Alternative 7: 97.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

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

      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 98.8%

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

      1. sub-neg 98.8%

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

      2. metadata-eval 98.8%

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

      3. distribute-lft-in 98.8%

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

      4. *-commutative 98.8%

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

      5. neg-mul-1 98.8%

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

      6. unsub-neg 98.8%

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

      7. associate-/l* 87.5%

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

      8. unpow2 87.5%

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

   7. Simplified 87.5%

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

      1. unpow2 87.5%

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

      2. associate-*l/ 98.8%

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

   9. Applied egg-rr 98.8%

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

       1. *-commutative 98.8%

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

       2. clear-num 98.7%

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

       3. un-div-inv 98.9%

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

   11. Applied egg-rr 98.9%

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

   if 1 < m

   1. Initial program 99.9%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. 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 inf 98.4%

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

      1. neg-mul-1 98.4%

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

      2. distribute-neg-frac2 98.4%

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

   7. Simplified 98.4%

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

4. Final simplification 98.6%

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

Alternative 8: 87.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

      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 98.8%

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

      1. sub-neg 98.8%

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

      2. metadata-eval 98.8%

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

      3. distribute-lft-in 98.8%

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

      4. *-commutative 98.8%

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

      5. neg-mul-1 98.8%

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

      6. unsub-neg 98.8%

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

      7. associate-/l* 87.5%

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

      8. unpow2 87.5%

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

   7. Simplified 87.5%

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

      1. unpow2 87.5%

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

      2. associate-*l/ 98.8%

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

   9. Applied egg-rr 98.8%

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

       1. *-commutative 98.8%

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

       2. clear-num 98.7%

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

       3. un-div-inv 98.9%

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

   11. Applied egg-rr 98.9%

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

   if 1 < m

   1. Initial program 99.9%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. 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 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. neg-mul-1 0.1%

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

      6. unsub-neg 0.1%

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

      7. associate-/l* 0.1%

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

      8. unpow2 0.1%

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

   7. Simplified 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*l/ 0.1%

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

   9. Applied egg-rr 0.1%

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

       1. frac-2neg 0.1%

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

       2. associate-*l/ 0.1%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 72.3%

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

       5. sqr-neg 72.3%

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

       6. sqrt-unprod 68.1%

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

       7. add-sqr-sqrt 68.1%

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

   11. Applied egg-rr 68.1%

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

4. Final simplification 83.4%

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

Alternative 9: 87.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	t_0 = m / (v / m)
	tmp = 0
	if m <= 1.0:
		tmp = t_0 - m
	else:
		tmp = -m - t_0
	return tmp

Julia

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

MATLAB

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

Wolfram

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

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

      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 98.8%

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

      1. sub-neg 98.8%

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

      2. metadata-eval 98.8%

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

      3. distribute-lft-in 98.8%

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

      4. *-commutative 98.8%

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

      5. neg-mul-1 98.8%

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

      6. unsub-neg 98.8%

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

      7. associate-/l* 87.5%

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

      8. unpow2 87.5%

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

   7. Simplified 87.5%

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

      1. unpow2 87.5%

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

      2. associate-*l/ 98.8%

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

   9. Applied egg-rr 98.8%

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

       1. *-commutative 98.8%

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

       2. clear-num 98.7%

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

       3. un-div-inv 98.9%

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

   11. Applied egg-rr 98.9%

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

   if 1 < m

   1. Initial program 99.9%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. 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 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. neg-mul-1 0.1%

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

      6. unsub-neg 0.1%

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

      7. associate-/l* 0.1%

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

      8. unpow2 0.1%

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

   7. Simplified 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*l/ 0.1%

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

   9. Applied egg-rr 0.1%

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

       1. add-sqr-sqrt 0.1%

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

       2. sqrt-unprod 0.1%

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

       3. sqr-neg 0.1%

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

       4. distribute-frac-neg2 0.1%

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

       5. distribute-frac-neg2 0.1%

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

       6. sqrt-unprod 0.0%

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

       7. add-sqr-sqrt 68.1%

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

       8. associate-/r/ 68.1%

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

       9. frac-2neg 68.1%

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

       10. distribute-frac-neg 68.1%

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

       11. remove-double-neg 68.1%

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

   11. Applied egg-rr 68.1%

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

4. Final simplification 83.4%

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

Alternative 10: 87.4% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

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

      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 98.8%

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

      1. sub-neg 98.8%

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

      2. metadata-eval 98.8%

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

      3. distribute-lft-in 98.8%

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

      4. *-commutative 98.8%

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

      5. neg-mul-1 98.8%

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

      6. unsub-neg 98.8%

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

      7. associate-/l* 87.5%

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

      8. unpow2 87.5%

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

   7. Simplified 87.5%

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

      1. unpow2 87.5%

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

      2. associate-*l/ 98.8%

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

   9. Applied egg-rr 98.8%

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

       1. *-commutative 98.8%

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

       2. clear-num 98.7%

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

       3. un-div-inv 98.9%

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

   11. Applied egg-rr 98.9%

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

   if 1 < m

   1. Initial program 99.9%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
   2. 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 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. neg-mul-1 0.1%

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

      6. unsub-neg 0.1%

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

      7. associate-/l* 0.1%

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

      8. unpow2 0.1%

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

   7. Simplified 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*l/ 0.1%

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

   9. Applied egg-rr 0.1%

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

       1. frac-2neg 0.1%

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

       2. associate-*l/ 0.1%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 72.3%

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

       5. sqr-neg 72.3%

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

       6. sqrt-unprod 68.1%

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

       7. add-sqr-sqrt 68.1%

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

   11. Applied egg-rr 68.1%

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

   12. Taylor expanded in m around 0 68.1%

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

       1. sub-neg 68.1%

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

       2. metadata-eval 68.1%

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

       3. +-commutative 68.1%

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

       4. mul-1-neg 68.1%

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

       5. unsub-neg 68.1%

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

   14. Simplified 68.1%

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

Alternative 11: 87.4% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

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

      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 98.8%

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

      1. sub-neg 98.8%

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

      2. metadata-eval 98.8%

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

      3. distribute-lft-in 98.8%

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

      4. *-commutative 98.8%

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

      5. neg-mul-1 98.8%

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

      6. unsub-neg 98.8%

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

      7. associate-/l* 87.5%

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

      8. unpow2 87.5%

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

   7. Simplified 87.5%

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

      1. unpow2 87.5%

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

      2. associate-*l/ 98.8%

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

   9. Applied egg-rr 98.8%

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

   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. Taylor expanded in m around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. neg-mul-1 0.1%

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

      6. unsub-neg 0.1%

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

      7. associate-/l* 0.1%

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

      8. unpow2 0.1%

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

   7. Simplified 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*l/ 0.1%

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

   9. Applied egg-rr 0.1%

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

       1. frac-2neg 0.1%

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

       2. associate-*l/ 0.1%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 72.3%

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

       5. sqr-neg 72.3%

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

       6. sqrt-unprod 68.1%

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

       7. add-sqr-sqrt 68.1%

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

   11. Applied egg-rr 68.1%

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

   12. Taylor expanded in m around 0 68.1%

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

       1. sub-neg 68.1%

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

       2. metadata-eval 68.1%

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

       3. +-commutative 68.1%

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

       4. mul-1-neg 68.1%

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

       5. unsub-neg 68.1%

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

   14. Simplified 68.1%

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

4. Final simplification 83.3%

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

Alternative 12: 87.4% 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. 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%

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

      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 98.8%

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

   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%

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

      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 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. neg-mul-1 0.1%

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

      6. unsub-neg 0.1%

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

      7. associate-/l* 0.1%

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

      8. unpow2 0.1%

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

   7. Simplified 0.1%

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

      1. unpow2 0.1%

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

      2. associate-*l/ 0.1%

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

   9. Applied egg-rr 0.1%

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

       1. frac-2neg 0.1%

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

       2. associate-*l/ 0.1%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 72.3%

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

       5. sqr-neg 72.3%

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

       6. sqrt-unprod 68.1%

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

       7. add-sqr-sqrt 68.1%

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

   11. Applied egg-rr 68.1%

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

   12. Taylor expanded in m around 0 68.1%

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

       1. sub-neg 68.1%

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

       2. metadata-eval 68.1%

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

       3. +-commutative 68.1%

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

       4. mul-1-neg 68.1%

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

       5. unsub-neg 68.1%

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

   14. Simplified 68.1%

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

4. Final simplification 83.3%

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

Alternative 13: 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* 99.8%

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

   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. 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 14: 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* 99.8%

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

   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. Final simplification 99.8%

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

Alternative 15: 36.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 6 \cdot 10^{-189}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= v 6e-189) (/ m (/ v m)) (- m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 6e-189) {
		tmp = m / (v / m);
	} 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 <= 6d-189) then
        tmp = m / (v / m)
    else
        tmp = -m
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (v <= 6e-189) {
		tmp = m / (v / m);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 6e-189:
		tmp = m / (v / m)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 6e-189)
		tmp = Float64(m / Float64(v / m));
	else
		tmp = Float64(-m);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (v <= 6e-189)
		tmp = m / (v / m);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 6e-189], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], (-m)]

Derivation

1. Split input into 2 regimes

2. if v < 6e-189

   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%

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

      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 46.3%

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

   6. Taylor expanded in m around inf 23.7%

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

      1. unpow2 31.2%

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

      2. associate-*l/ 46.4%

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

   8. Applied egg-rr 36.4%

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

      1. *-commutative 46.4%

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

      2. clear-num 46.3%

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

      3. un-div-inv 46.4%

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

   10. Applied egg-rr 36.5%

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

   if 6e-189 < 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 43.8%

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

      1. neg-mul-1 43.8%

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

   7. Simplified 43.8%

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

Alternative 16: 36.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq 1.35 \cdot 10^{-188}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= v 1.35e-188) (* m (/ m v)) (- m)))

C

double code(double m, double v) {
	double tmp;
	if (v <= 1.35e-188) {
		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 <= 1.35d-188) 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 <= 1.35e-188) {
		tmp = m * (m / v);
	} else {
		tmp = -m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if v <= 1.35e-188:
		tmp = m * (m / v)
	else:
		tmp = -m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (v <= 1.35e-188)
		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 <= 1.35e-188)
		tmp = m * (m / v);
	else
		tmp = -m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[v, 1.35e-188], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision], (-m)]

Derivation

1. Split input into 2 regimes

2. if v < 1.35e-188

   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%

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

      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 46.3%

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

   6. Taylor expanded in m around inf 23.7%

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

      1. unpow2 31.2%

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

      2. associate-*l/ 46.4%

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

   8. Applied egg-rr 36.4%

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

   if 1.35e-188 < 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 43.8%

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

      1. neg-mul-1 43.8%

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

   7. Simplified 43.8%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq 1.35 \cdot 10^{-188}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-m\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.8% 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* 99.8%

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

   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 32.0%

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

   1. neg-mul-1 32.0%

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

7. Simplified 32.0%

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

Reproduce

herbie shell --seed 2024103 
(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))