b parameter of renormalized beta distribution

Percentage Accurate: 99.9% → 99.9%

Time: 5.7s

Alternatives: 9

Speedup: N/A×

• 41.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

code[m_, v_] := If[LessEqual[m, 1.0], N[(N[(1.0 - m), $MachinePrecision] * N[(N[(m / v), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - m), $MachinePrecision] * 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 100.0%

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

   2. Taylor expanded in m around 0 98.6%

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

   if 1 < m

   1. Initial program 99.8%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in m around inf 97.4%

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

      1. neg-mul-1 97.4%

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

      2. distribute-neg-frac 97.4%

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

   6. Simplified 97.4%

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

4. Final simplification 97.9%

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

Alternative 3: 61.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 5.4 \cdot 10^{-204}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 8.8 \cdot 10^{-172} \lor \neg \left(m \leq 1.12 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 5.4e-204)
   -1.0
   (if (or (<= m 8.8e-172) (not (<= m 1.12e-125))) (/ m v) -1.0)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 5.4e-204) {
		tmp = -1.0;
	} else if ((m <= 8.8e-172) || !(m <= 1.12e-125)) {
		tmp = m / v;
	} else {
		tmp = -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 <= 5.4d-204) then
        tmp = -1.0d0
    else if ((m <= 8.8d-172) .or. (.not. (m <= 1.12d-125))) then
        tmp = m / v
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 5.4e-204) {
		tmp = -1.0;
	} else if ((m <= 8.8e-172) || !(m <= 1.12e-125)) {
		tmp = m / v;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 5.4e-204:
		tmp = -1.0
	elif (m <= 8.8e-172) or not (m <= 1.12e-125):
		tmp = m / v
	else:
		tmp = -1.0
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 5.4e-204)
		tmp = -1.0;
	elseif ((m <= 8.8e-172) || !(m <= 1.12e-125))
		tmp = Float64(m / v);
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 5.4e-204)
		tmp = -1.0;
	elseif ((m <= 8.8e-172) || ~((m <= 1.12e-125)))
		tmp = m / v;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 5.4e-204], -1.0, If[Or[LessEqual[m, 8.8e-172], N[Not[LessEqual[m, 1.12e-125]], $MachinePrecision]], N[(m / v), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if m < 5.39999999999999983e-204 or 8.80000000000000036e-172 < m < 1.11999999999999997e-125

   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%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 80.8%

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

   if 5.39999999999999983e-204 < m < 8.80000000000000036e-172 or 1.11999999999999997e-125 < m

   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. associate-*r/ 99.7%

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

      3. fma-neg 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in m around 0 68.4%

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

   5. Taylor expanded in v around 0 92.9%

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

   6. Taylor expanded in m around 0 56.2%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 5.4 \cdot 10^{-204}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 8.8 \cdot 10^{-172} \lor \neg \left(m \leq 1.12 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 87.2% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 2.39999999999999991

   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%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 98.3%

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

      1. +-commutative 98.3%

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

      2. distribute-lft-in 98.3%

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

      3. div-inv 98.6%

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

      4. *-rgt-identity 98.6%

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

   6. Applied egg-rr 98.6%

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

      1. add-sqr-sqrt 98.6%

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

      2. sqrt-unprod 98.6%

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

      3. sqr-neg 98.6%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 98.6%

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

      6. sub-neg 98.6%

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

   8. Applied egg-rr 98.6%

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

   if 2.39999999999999991 < 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 0.1%

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

      1. *-commutative 0.1%

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

      2. sub-neg 0.1%

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

      3. distribute-rgt-in 0.1%

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

      4. clear-num 0.1%

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

      5. associate-/r/ 0.1%

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

      6. associate-/r* 0.1%

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

      7. clear-num 0.1%

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

      8. sub-neg 0.1%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 72.8%

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

      11. sqr-neg 72.8%

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

      12. sqrt-unprod 72.8%

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

      13. add-sqr-sqrt 72.8%

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

      14. +-commutative 72.8%

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

      15. distribute-rgt-out 72.8%

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

      16. *-un-lft-identity 72.8%

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

      17. fma-def 72.8%

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

      18. metadata-eval 72.8%

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

      19. sub-neg 72.8%

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

      20. add-sqr-sqrt 0.0%

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

      21. sqrt-unprod 26.7%

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

      22. sqr-neg 26.7%

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

   4. Applied egg-rr 72.8%

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

      1. *-lft-identity 72.8%

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

      2. *-lft-identity 72.8%

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

      3. fma-udef 72.8%

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

      4. *-rgt-identity 72.8%

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

      5. distribute-lft-in 72.8%

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

      6. +-commutative 72.8%

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

      7. associate-*l/ 72.8%

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

      8. distribute-rgt-in 72.8%

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

      9. +-commutative 72.8%

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

   6. Simplified 72.8%

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

   7. Taylor expanded in v around 0 72.8%

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

      1. associate-/l* 72.8%

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

      2. +-commutative 72.8%

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

   9. Simplified 72.8%

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

4. Final simplification 84.4%

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

Alternative 5: 87.2% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := N[(N[(1.0 + m), $MachinePrecision] * N[(N[(m / v), $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. Taylor expanded in m around 0 44.4%

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

   1. *-commutative 44.4%

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

   2. sub-neg 44.4%

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

   3. distribute-rgt-in 44.4%

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

   4. clear-num 44.2%

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

   5. associate-/r/ 44.2%

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

   6. associate-/r* 44.2%

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

   7. clear-num 44.4%

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

   8. sub-neg 44.4%

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

   9. add-sqr-sqrt 0.0%

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

   10. sqrt-unprod 84.4%

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

   11. sqr-neg 84.4%

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

   12. sqrt-unprod 84.4%

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

   13. add-sqr-sqrt 84.4%

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

   14. +-commutative 84.4%

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

   15. distribute-rgt-out 84.4%

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

   16. *-un-lft-identity 84.4%

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

   17. fma-def 84.4%

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

   18. metadata-eval 84.4%

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

   19. sub-neg 84.4%

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

   20. add-sqr-sqrt 0.0%

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

   21. sqrt-unprod 59.0%

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

   22. sqr-neg 59.0%

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

4. Applied egg-rr 84.4%

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

   1. *-lft-identity 84.4%

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

   2. *-lft-identity 84.4%

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

   3. fma-udef 84.4%

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

   4. *-rgt-identity 84.4%

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

   5. distribute-lft-in 84.4%

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

   6. +-commutative 84.4%

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

   7. associate-*l/ 84.4%

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

   8. distribute-rgt-in 84.4%

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

   9. +-commutative 84.4%

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

6. Simplified 84.4%

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

7. Final simplification 84.4%

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

Alternative 6: 76.2% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in m around 0 71.1%

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

   1. +-commutative 71.1%

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

   2. distribute-lft-in 71.1%

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

   3. div-inv 71.2%

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

   4. *-rgt-identity 71.2%

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

6. Applied egg-rr 71.2%

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

   1. add-sqr-sqrt 71.2%

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

   2. sqrt-unprod 78.4%

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

   3. sqr-neg 78.4%

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

   4. sqrt-unprod 0.0%

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

   5. add-sqr-sqrt 71.2%

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

   6. sub-neg 71.2%

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

8. Applied egg-rr 71.2%

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

9. Final simplification 71.2%

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

Alternative 7: 76.2% accurate, 2.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in m around 0 71.1%

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

   1. +-commutative 71.1%

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

   2. distribute-lft-in 71.1%

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

   3. div-inv 71.2%

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

   4. *-rgt-identity 71.2%

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

6. Applied egg-rr 71.2%

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

   1. add-sqr-sqrt 71.2%

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

   2. sqrt-unprod 78.4%

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

   3. sqr-neg 78.4%

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

   4. sqrt-unprod 0.0%

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

   5. add-sqr-sqrt 71.2%

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

   6. sub-neg 71.2%

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

8. Applied egg-rr 71.2%

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

9. Taylor expanded in v around 0 71.2%

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

10. Final simplification 71.2%

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

Alternative 8: 27.1% 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%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in v around inf 25.9%

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

   1. neg-mul-1 25.9%

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

   2. neg-sub0 25.9%

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

   3. associate--r- 25.9%

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

   4. metadata-eval 25.9%

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

6. Simplified 25.9%

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

7. Final simplification 25.9%

   \[\leadsto m + -1 \]

Alternative 9: 24.7% 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%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in m around 0 23.3%

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

5. Final simplification 23.3%

   \[\leadsto -1 \]

Reproduce

herbie shell --seed 2023308 
(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)))