b parameter of renormalized beta distribution

Percentage Accurate: 99.9% → 99.9%

Time: 5.8s

Alternatives: 14

Speedup: 1.0×

• 40.9% 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

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

FPCore

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

C

double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * (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) * (1.0d0 - m)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * (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) * (1.0d0 - m)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in m around 0 99.9%

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

   1. mul-1-neg 99.9%

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

   2. unpow2 99.9%

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

   3. distribute-lft-neg-out 99.9%

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

   4. +-commutative 99.9%

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

   5. distribute-lft-neg-out 99.9%

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

   6. unpow2 99.9%

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

   7. unsub-neg 99.9%

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

   8. unpow2 99.9%

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

4. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.28 \cdot 10^{-20}:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(m \cdot \frac{1 - m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.28e-20)
   (+ -1.0 (+ m (/ m v)))
   (* (- 1.0 m) (* m (/ (- 1.0 m) v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.28e-20) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (1.0 - m) * (m * ((1.0 - m) / v));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.28d-20) then
        tmp = (-1.0d0) + (m + (m / v))
    else
        tmp = (1.0d0 - m) * (m * ((1.0d0 - m) / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.28e-20) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (1.0 - m) * (m * ((1.0 - m) / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.28e-20:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = (1.0 - m) * (m * ((1.0 - m) / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.28e-20)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(Float64(1.0 - m) * Float64(m * Float64(Float64(1.0 - m) / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.28e-20)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = (1.0 - m) * (m * ((1.0 - m) / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.28e-20], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - m), $MachinePrecision] * N[(m * N[(N[(1.0 - m), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.2800000000000001e-20

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. +-commutative 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. *-lft-identity 99.8%

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

      7. associate-*l/ 100.0%

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

      8. *-lft-identity 100.0%

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

   6. Simplified 100.0%

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

   if 1.2800000000000001e-20 < m

   1. Initial program 99.8%

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

   2. Taylor expanded in m around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unpow2 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. unpow2 99.9%

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

      7. unsub-neg 99.9%

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

      8. unpow2 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.8%

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

      1. associate-/l* 99.8%

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

      2. unpow2 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in v around 0 99.8%

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

      1. *-commutative 99.8%

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

      2. unpow2 99.8%

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

      3. associate-*r/ 99.8%

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

      4. cancel-sign-sub-inv 99.8%

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

      5. *-lft-identity 99.8%

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

      6. distribute-rgt-in 99.8%

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

      7. sub-neg 99.8%

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

      8. associate-*r/ 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.28 \cdot 10^{-20}:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(m \cdot \frac{1 - m}{v}\right)\\ \end{array} \]

Alternative 3: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 6.4 \cdot 10^{-46}:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(m - m \cdot m\right) \cdot \left(1 - m\right)}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 6.4e-46) (+ -1.0 (+ m (/ m v))) (/ (* (- m (* m m)) (- 1.0 m)) v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 6.4e-46) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = ((m - (m * m)) * (1.0 - m)) / v;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 6.4d-46) then
        tmp = (-1.0d0) + (m + (m / v))
    else
        tmp = ((m - (m * m)) * (1.0d0 - m)) / v
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 6.4e-46) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = ((m - (m * m)) * (1.0 - m)) / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 6.4e-46:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = ((m - (m * m)) * (1.0 - m)) / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 6.4e-46)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(Float64(Float64(m - Float64(m * m)) * Float64(1.0 - m)) / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 6.4e-46)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = ((m - (m * m)) * (1.0 - m)) / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 6.4e-46], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(m - N[(m * m), $MachinePrecision]), $MachinePrecision] * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 6.3999999999999998e-46

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. +-commutative 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. *-lft-identity 99.8%

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

      7. associate-*l/ 100.0%

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

      8. *-lft-identity 100.0%

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

   6. Simplified 100.0%

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

   if 6.3999999999999998e-46 < m

   1. Initial program 99.8%

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

   2. Taylor expanded in m around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unpow2 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. unpow2 99.9%

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

      7. unsub-neg 99.9%

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

      8. unpow2 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.8%

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

      1. unpow2 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 6.4 \cdot 10^{-46}:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(m - m \cdot m\right) \cdot \left(1 - m\right)}{v}\\ \end{array} \]

Alternative 4: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 5 \cdot 10^{-46}:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m - m \cdot m}{\frac{v}{1 - m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 5e-46) (+ -1.0 (+ m (/ m v))) (/ (- m (* m m)) (/ v (- 1.0 m)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 5e-46) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m - (m * m)) / (v / (1.0 - m));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 5d-46) then
        tmp = (-1.0d0) + (m + (m / v))
    else
        tmp = (m - (m * m)) / (v / (1.0d0 - m))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 5e-46) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m - (m * m)) / (v / (1.0 - m));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 5e-46:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = (m - (m * m)) / (v / (1.0 - m))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 5e-46)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(Float64(m - Float64(m * m)) / Float64(v / Float64(1.0 - m)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 5e-46)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = (m - (m * m)) / (v / (1.0 - m));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 5e-46], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m - N[(m * m), $MachinePrecision]), $MachinePrecision] / N[(v / N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 4.99999999999999992e-46

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. +-commutative 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. *-lft-identity 99.8%

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

      7. associate-*l/ 100.0%

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

      8. *-lft-identity 100.0%

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

   6. Simplified 100.0%

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

   if 4.99999999999999992e-46 < m

   1. Initial program 99.8%

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

   2. Taylor expanded in m around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unpow2 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. unpow2 99.9%

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

      7. unsub-neg 99.9%

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

      8. unpow2 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.8%

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

      1. associate-/l* 99.8%

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

      2. unpow2 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 5 \cdot 10^{-46}:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m - m \cdot m}{\frac{v}{1 - m}}\\ \end{array} \]

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double m, double v) {
	return (1.0 - 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 = (1.0d0 - m) * ((m / (v / (1.0d0 - m))) + (-1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-/l* 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 6: 98.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.4:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(m + -2\right) \cdot \left(m \cdot \frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.4) (+ -1.0 (+ m (/ m v))) (* (+ m -2.0) (* m (/ m v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.4) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m + -2.0) * (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 <= 2.4d0) then
        tmp = (-1.0d0) + (m + (m / v))
    else
        tmp = (m + (-2.0d0)) * (m * (m / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 2.4) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m + -2.0) * (m * (m / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.4:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = (m + -2.0) * (m * (m / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.4)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(Float64(m + -2.0) * Float64(m * Float64(m / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.4)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = (m + -2.0) * (m * (m / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.4], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m + -2.0), $MachinePrecision] * N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.39999999999999991

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 97.5%

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

      1. sub-neg 97.5%

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

      2. metadata-eval 97.5%

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

      3. +-commutative 97.5%

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

      4. *-commutative 97.5%

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

      5. distribute-rgt-in 97.5%

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

      6. *-lft-identity 97.5%

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

      7. associate-*l/ 97.7%

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

      8. *-lft-identity 97.7%

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

   6. Simplified 97.7%

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

   if 2.39999999999999991 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unpow2 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. unpow2 99.9%

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

      7. unsub-neg 99.9%

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

      8. unpow2 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

      1. unpow2 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in m around inf 24.1%

      \[\leadsto \color{blue}{-2 \cdot \frac{{m}^{2}}{v} + \frac{{m}^{3}}{v}} \]
   9. Step-by-step derivation

      1. +-commutative 24.1%

         \[\leadsto \color{blue}{\frac{{m}^{3}}{v} + -2 \cdot \frac{{m}^{2}}{v}} \]

      2. cube-mult 24.1%

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

      3. associate-*l/ 24.1%

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

      4. associate-*r* 24.0%

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

      5. *-commutative 24.0%

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

      6. unpow2 24.0%

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

      7. associate-*l/ 24.0%

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

      8. distribute-lft-out 98.8%

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

      9. *-commutative 98.8%

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

   10. Simplified 98.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.4:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(m + -2\right) \cdot \left(m \cdot \frac{m}{v}\right)\\ \end{array} \]

Alternative 7: 98.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.62:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(m + -2\right) \cdot \left(m \cdot \frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.62) (* (- 1.0 m) (+ -1.0 (/ m v))) (* (+ m -2.0) (* m (/ m v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.62) {
		tmp = (1.0 - m) * (-1.0 + (m / v));
	} else {
		tmp = (m + -2.0) * (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 <= 1.62d0) then
        tmp = (1.0d0 - m) * ((-1.0d0) + (m / v))
    else
        tmp = (m + (-2.0d0)) * (m * (m / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.62) {
		tmp = (1.0 - m) * (-1.0 + (m / v));
	} else {
		tmp = (m + -2.0) * (m * (m / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.62:
		tmp = (1.0 - m) * (-1.0 + (m / v))
	else:
		tmp = (m + -2.0) * (m * (m / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.62)
		tmp = Float64(Float64(1.0 - m) * Float64(-1.0 + Float64(m / v)));
	else
		tmp = Float64(Float64(m + -2.0) * Float64(m * Float64(m / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.62)
		tmp = (1.0 - m) * (-1.0 + (m / v));
	else
		tmp = (m + -2.0) * (m * (m / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.62], N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m + -2.0), $MachinePrecision] * N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.6200000000000001

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 97.8%

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

   if 1.6200000000000001 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unpow2 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. unpow2 99.9%

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

      7. unsub-neg 99.9%

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

      8. unpow2 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

      1. unpow2 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in m around inf 24.1%

      \[\leadsto \color{blue}{-2 \cdot \frac{{m}^{2}}{v} + \frac{{m}^{3}}{v}} \]
   9. Step-by-step derivation

      1. +-commutative 24.1%

         \[\leadsto \color{blue}{\frac{{m}^{3}}{v} + -2 \cdot \frac{{m}^{2}}{v}} \]

      2. cube-mult 24.1%

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

      3. associate-*l/ 24.1%

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

      4. associate-*r* 24.0%

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

      5. *-commutative 24.0%

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

      6. unpow2 24.0%

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

      7. associate-*l/ 24.0%

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

      8. distribute-lft-out 98.8%

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

      9. *-commutative 98.8%

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

   10. Simplified 98.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.62:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(m + -2\right) \cdot \left(m \cdot \frac{m}{v}\right)\\ \end{array} \]

Alternative 8: 98.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.62:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(m \cdot \left(m + -2\right)\right)}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.62) (* (- 1.0 m) (+ -1.0 (/ m v))) (/ (* m (* m (+ m -2.0))) v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.62) {
		tmp = (1.0 - m) * (-1.0 + (m / v));
	} else {
		tmp = (m * (m * (m + -2.0))) / v;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.62d0) then
        tmp = (1.0d0 - m) * ((-1.0d0) + (m / v))
    else
        tmp = (m * (m * (m + (-2.0d0)))) / v
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.62) {
		tmp = (1.0 - m) * (-1.0 + (m / v));
	} else {
		tmp = (m * (m * (m + -2.0))) / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.62:
		tmp = (1.0 - m) * (-1.0 + (m / v))
	else:
		tmp = (m * (m * (m + -2.0))) / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.62)
		tmp = Float64(Float64(1.0 - m) * Float64(-1.0 + Float64(m / v)));
	else
		tmp = Float64(Float64(m * Float64(m * Float64(m + -2.0))) / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.62)
		tmp = (1.0 - m) * (-1.0 + (m / v));
	else
		tmp = (m * (m * (m + -2.0))) / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.62], N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m * N[(m * N[(m + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.6200000000000001

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 97.8%

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

   if 1.6200000000000001 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unpow2 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. unpow2 99.9%

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

      7. unsub-neg 99.9%

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

      8. unpow2 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

      1. associate-/l* 99.9%

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

      2. unpow2 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in m around inf 24.1%

      \[\leadsto \color{blue}{-2 \cdot \frac{{m}^{2}}{v} + \frac{{m}^{3}}{v}} \]
   9. Step-by-step derivation

      1. +-commutative 24.1%

         \[\leadsto \color{blue}{\frac{{m}^{3}}{v} + -2 \cdot \frac{{m}^{2}}{v}} \]

      2. cube-mult 24.1%

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

      3. associate-*r/ 24.0%

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

      4. unpow2 24.0%

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

      5. distribute-rgt-in 98.8%

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

      6. associate-*l/ 98.9%

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

      7. associate-*r* 98.9%

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

   10. Simplified 98.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.62:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(m \cdot \left(m + -2\right)\right)}{v}\\ \end{array} \]

Alternative 9: 72.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 3.7 \cdot 10^{-196}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 2.2:\\ \;\;\;\;\frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 3.7e-196) -1.0 (if (<= m 2.2) (/ m v) (* m (/ m v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 3.7e-196) {
		tmp = -1.0;
	} else if (m <= 2.2) {
		tmp = m / v;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 3.7d-196) then
        tmp = -1.0d0
    else if (m <= 2.2d0) then
        tmp = m / v
    else
        tmp = m * (m / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 3.7e-196) {
		tmp = -1.0;
	} else if (m <= 2.2) {
		tmp = m / v;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 3.7e-196:
		tmp = -1.0
	elif m <= 2.2:
		tmp = m / v
	else:
		tmp = m * (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 3.7e-196)
		tmp = -1.0;
	elseif (m <= 2.2)
		tmp = Float64(m / v);
	else
		tmp = Float64(m * Float64(m / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 3.7e-196)
		tmp = -1.0;
	elseif (m <= 2.2)
		tmp = m / v;
	else
		tmp = m * (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 3.7e-196], -1.0, If[LessEqual[m, 2.2], N[(m / v), $MachinePrecision], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 3.7000000000000001e-196

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 88.3%

      \[\leadsto \color{blue}{-1} \]

   if 3.7000000000000001e-196 < m < 2.2000000000000002

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unpow2 100.0%

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

      3. distribute-lft-neg-out 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. unpow2 100.0%

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

      7. unsub-neg 100.0%

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

      8. unpow2 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in v around 0 77.3%

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

      1. unpow2 77.3%

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

   7. Simplified 77.3%

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

   8. Taylor expanded in m around 0 73.8%

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

   if 2.2000000000000002 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. distribute-rgt-in 0.1%

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

      3. *-un-lft-identity 0.1%

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

      4. sub-neg 0.1%

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

      5. metadata-eval 0.1%

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

      6. add-sqr-sqrt 0.0%

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

      7. sqrt-unprod 77.1%

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

      8. sqr-neg 77.1%

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

      9. sqrt-prod 77.1%

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

      10. add-sqr-sqrt 77.1%

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

      11. sub-neg 77.1%

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

      12. metadata-eval 77.1%

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

   4. Applied egg-rr 77.1%

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

      1. distribute-rgt1-in 77.1%

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

   6. Simplified 77.1%

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

   7. Taylor expanded in m around inf 77.1%

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

      1. unpow2 77.1%

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

      2. associate-*r/ 77.1%

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

   9. Simplified 77.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 3.7 \cdot 10^{-196}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 2.2:\\ \;\;\;\;\frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]

Alternative 10: 72.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 8.5 \cdot 10^{-197}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 8.5e-197) -1.0 (* (/ m v) (+ m 1.0))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 8.5e-197) {
		tmp = -1.0;
	} else {
		tmp = (m / v) * (m + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 8.5d-197) then
        tmp = -1.0d0
    else
        tmp = (m / v) * (m + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 8.5e-197) {
		tmp = -1.0;
	} else {
		tmp = (m / v) * (m + 1.0);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 8.5e-197:
		tmp = -1.0
	else:
		tmp = (m / v) * (m + 1.0)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 8.5e-197)
		tmp = -1.0;
	else
		tmp = Float64(Float64(m / v) * Float64(m + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 8.5e-197)
		tmp = -1.0;
	else
		tmp = (m / v) * (m + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 8.5e-197], -1.0, N[(N[(m / v), $MachinePrecision] * N[(m + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 8.5e-197

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 88.3%

      \[\leadsto \color{blue}{-1} \]

   if 8.5e-197 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 37.3%

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

      1. sub-neg 37.3%

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

      2. distribute-rgt-in 37.3%

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

      3. *-un-lft-identity 37.3%

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

      4. sub-neg 37.3%

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

      5. metadata-eval 37.3%

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

      6. add-sqr-sqrt 0.0%

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

      7. sqrt-unprod 84.5%

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

      8. sqr-neg 84.5%

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

      9. sqrt-prod 84.5%

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

      10. add-sqr-sqrt 84.5%

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

      11. sub-neg 84.5%

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

      12. metadata-eval 84.5%

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

   4. Applied egg-rr 84.5%

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

      1. distribute-rgt1-in 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in v around 0 75.8%

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

      1. associate-/l* 75.8%

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

      2. associate-/r/ 75.8%

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

      3. +-commutative 75.8%

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

   9. Applied egg-rr 75.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 8.5 \cdot 10^{-197}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m + 1\right)\\ \end{array} \]

Alternative 11: 87.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.35:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.35) (+ -1.0 (+ m (/ m v))) (* (/ m v) (+ m 1.0))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.35) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m / v) * (m + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 2.35d0) then
        tmp = (-1.0d0) + (m + (m / v))
    else
        tmp = (m / v) * (m + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 2.35) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m / v) * (m + 1.0);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.35:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = (m / v) * (m + 1.0)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.35)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(Float64(m / v) * Float64(m + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.35)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = (m / v) * (m + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.35], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m / v), $MachinePrecision] * N[(m + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.35000000000000009

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 97.5%

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

      1. sub-neg 97.5%

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

      2. metadata-eval 97.5%

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

      3. +-commutative 97.5%

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

      4. *-commutative 97.5%

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

      5. distribute-rgt-in 97.5%

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

      6. *-lft-identity 97.5%

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

      7. associate-*l/ 97.7%

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

      8. *-lft-identity 97.7%

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

   6. Simplified 97.7%

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

   if 2.35000000000000009 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. distribute-rgt-in 0.1%

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

      3. *-un-lft-identity 0.1%

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

      4. sub-neg 0.1%

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

      5. metadata-eval 0.1%

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

      6. add-sqr-sqrt 0.0%

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

      7. sqrt-unprod 77.1%

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

      8. sqr-neg 77.1%

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

      9. sqrt-prod 77.1%

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

      10. add-sqr-sqrt 77.1%

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

      11. sub-neg 77.1%

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

      12. metadata-eval 77.1%

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

   4. Applied egg-rr 77.1%

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

      1. distribute-rgt1-in 77.1%

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

   6. Simplified 77.1%

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

   7. Taylor expanded in v around 0 77.1%

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

      1. associate-/l* 77.1%

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

      2. associate-/r/ 77.1%

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

      3. +-commutative 77.1%

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

   9. Applied egg-rr 77.1%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.35:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m + 1\right)\\ \end{array} \]

Alternative 12: 61.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 3.7 \cdot 10^{-196}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= m 3.7e-196) -1.0 (/ m v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 3.7e-196) {
		tmp = -1.0;
	} else {
		tmp = 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 <= 3.7d-196) then
        tmp = -1.0d0
    else
        tmp = m / v
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 3.7e-196) {
		tmp = -1.0;
	} else {
		tmp = m / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 3.7e-196:
		tmp = -1.0
	else:
		tmp = m / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 3.7e-196)
		tmp = -1.0;
	else
		tmp = Float64(m / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 3.7e-196)
		tmp = -1.0;
	else
		tmp = m / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 3.7e-196], -1.0, N[(m / v), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 3.7000000000000001e-196

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 88.3%

      \[\leadsto \color{blue}{-1} \]

   if 3.7000000000000001e-196 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unpow2 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. unpow2 99.9%

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

      7. unsub-neg 99.9%

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

      8. unpow2 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in v around 0 91.2%

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

      1. unpow2 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in m around 0 58.6%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 3.7 \cdot 10^{-196}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v}\\ \end{array} \]

Alternative 13: 27.6% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ m + -1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-/l* 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in v around inf 26.1%

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

   1. neg-mul-1 26.1%

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

   2. neg-sub0 26.1%

      \[\leadsto \color{blue}{0 - \left(1 - m\right)} \]

   3. associate--r- 26.1%

      \[\leadsto \color{blue}{\left(0 - 1\right) + m} \]

   4. metadata-eval 26.1%

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

6. Simplified 26.1%

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

7. Final simplification 26.1%

   \[\leadsto m + -1 \]

Alternative 14: 25.2% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	return -1.0

Julia

function code(m, v)
	return -1.0
end

MATLAB

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

Wolfram

code[m_, v_] := -1.0

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-/l* 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in m around 0 23.7%

   \[\leadsto \color{blue}{-1} \]

5. Final simplification 23.7%

   \[\leadsto -1 \]

Reproduce

herbie shell --seed 2023252 
(FPCore (m v)
  :name "b 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) (- 1.0 m)))