b parameter of renormalized beta distribution

Percentage Accurate: 99.9% → 99.9%

Time: 8.5s

Alternatives: 10

Speedup: 1.0×

• 42.5% 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. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 99.9%

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

   2. associate-*r/ 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 7.4 \cdot 10^{-190}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1.9 \cdot 10^{-168} \lor \neg \left(m \leq 6.8 \cdot 10^{-136}\right):\\ \;\;\;\;m + \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 7.4e-190)
   -1.0
   (if (or (<= m 1.9e-168) (not (<= m 6.8e-136))) (+ m (/ m v)) -1.0)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 7.4e-190) {
		tmp = -1.0;
	} else if ((m <= 1.9e-168) || !(m <= 6.8e-136)) {
		tmp = m + (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 <= 7.4d-190) then
        tmp = -1.0d0
    else if ((m <= 1.9d-168) .or. (.not. (m <= 6.8d-136))) then
        tmp = m + (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 <= 7.4e-190) {
		tmp = -1.0;
	} else if ((m <= 1.9e-168) || !(m <= 6.8e-136)) {
		tmp = m + (m / v);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 7.4e-190:
		tmp = -1.0
	elif (m <= 1.9e-168) or not (m <= 6.8e-136):
		tmp = m + (m / v)
	else:
		tmp = -1.0
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 7.4e-190)
		tmp = -1.0;
	elseif ((m <= 1.9e-168) || !(m <= 6.8e-136))
		tmp = Float64(m + Float64(m / v));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 7.4e-190)
		tmp = -1.0;
	elseif ((m <= 1.9e-168) || ~((m <= 6.8e-136)))
		tmp = m + (m / v);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 7.4e-190], -1.0, If[Or[LessEqual[m, 1.9e-168], N[Not[LessEqual[m, 6.8e-136]], $MachinePrecision]], N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if m < 7.4000000000000004e-190 or 1.9e-168 < m < 6.8000000000000001e-136

   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* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 81.7%

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

   if 7.4000000000000004e-190 < m < 1.9e-168 or 6.8000000000000001e-136 < 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. *-commutative 99.9%

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

      3. associate-/l* 99.9%

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

      4. fma-neg 99.9%

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

      5. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 31.0%

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

   6. Taylor expanded in m around inf 23.3%

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

      1. +-commutative 23.3%

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

      2. distribute-rgt-in 23.3%

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

      3. *-lft-identity 23.3%

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

      4. associate-+l+ 23.3%

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

      5. associate-/r/ 23.3%

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

      6. neg-mul-1 23.3%

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

      7. distribute-frac-neg 23.3%

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

      8. unpow2 23.3%

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

      9. distribute-rgt-neg-out 23.3%

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

      10. associate-*l/ 23.3%

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

      11. distribute-rgt-neg-out 23.3%

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

      12. associate-/r/ 23.3%

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

      13. sub-neg 23.3%

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

      14. div-sub 23.3%

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

      15. associate-/r/ 23.3%

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

      16. *-commutative 23.3%

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

   8. Simplified 23.3%

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

   9. Taylor expanded in m around 0 57.0%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 7.4 \cdot 10^{-190}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1.9 \cdot 10^{-168} \lor \neg \left(m \leq 6.8 \cdot 10^{-136}\right):\\ \;\;\;\;m + \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.0% accurate, 0.8× 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. 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. *-commutative 100.0%

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

      3. associate-/l* 100.0%

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

      4. fma-neg 100.0%

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

      5. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in m around 0 98.9%

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

   if 1 < m

   1. Initial program 99.9%

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

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around inf 99.0%

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

      1. neg-mul-1 99.0%

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

      2. distribute-neg-frac2 99.0%

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

   7. Simplified 99.0%

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

4. Final simplification 98.9%

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

Alternative 4: 87.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.3:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(1 + \frac{1 + m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.3) (+ -1.0 (+ m (/ m v))) (* m (+ 1.0 (/ (+ 1.0 m) v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.3) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = m * (1.0 + ((1.0 + m) / v));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 2.3d0) then
        tmp = (-1.0d0) + (m + (m / v))
    else
        tmp = m * (1.0d0 + ((1.0d0 + m) / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 2.3) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = m * (1.0 + ((1.0 + m) / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.3:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = m * (1.0 + ((1.0 + m) / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.3)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(m * Float64(1.0 + Float64(Float64(1.0 + m) / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.3)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = m * (1.0 + ((1.0 + m) / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.3], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(m * N[(1.0 + N[(N[(1.0 + m), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.2999999999999998

   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* 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in m around 0 98.7%

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

      1. +-commutative 98.7%

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

      2. distribute-lft-in 98.7%

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

      3. div-inv 98.8%

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

      4. *-rgt-identity 98.8%

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

   7. Applied egg-rr 98.8%

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

   if 2.2999999999999998 < 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. *-commutative 99.9%

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

      3. associate-/l* 99.9%

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

      4. fma-neg 99.9%

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

      5. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 0.1%

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

   6. Taylor expanded in m around inf 0.1%

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

      1. +-commutative 0.1%

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

      2. distribute-rgt-in 0.1%

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

      3. *-lft-identity 0.1%

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

      4. associate-+l+ 0.1%

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

      5. associate-/r/ 0.1%

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

      6. neg-mul-1 0.1%

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

      7. distribute-frac-neg 0.1%

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

      8. unpow2 0.1%

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

      9. distribute-rgt-neg-out 0.1%

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

      10. associate-*l/ 0.1%

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

      11. distribute-rgt-neg-out 0.1%

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

      12. associate-/r/ 0.1%

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

      13. sub-neg 0.1%

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

      14. div-sub 0.1%

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

      15. associate-/r/ 0.1%

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

      16. *-commutative 0.1%

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

   8. Simplified 0.1%

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

      1. *-commutative 0.1%

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

      2. distribute-rgt1-in 0.1%

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

      3. *-un-lft-identity 0.1%

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

      4. *-un-lft-identity 0.1%

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

      5. sub-neg 0.1%

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

      6. +-commutative 0.1%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 75.0%

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

      9. sqr-neg 75.0%

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

      10. sqrt-unprod 75.0%

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

      11. add-sqr-sqrt 75.0%

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

   10. Applied egg-rr 75.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.3:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(1 + \frac{1 + m}{v}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.4% accurate, 0.9× speedup

Math

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

FPCore

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

Fortran

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

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.0) {
		tmp = (1.0 - m) * ((m / v) + -1.0);
	} else {
		tmp = m * (1.0 + ((1.0 + 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 = m * (1.0 + ((1.0 + 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(m * Float64(1.0 + Float64(Float64(1.0 + 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 = m * (1.0 + ((1.0 + 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[(m * N[(1.0 + N[(N[(1.0 + m), $MachinePrecision] / v), $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. 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. *-commutative 100.0%

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

      3. associate-/l* 100.0%

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

      4. fma-neg 100.0%

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

      5. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in m around 0 98.9%

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

   if 1 < m

   1. Initial program 99.9%

      \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right) \]
   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. *-commutative 99.9%

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

      3. associate-/l* 99.9%

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

      4. fma-neg 99.9%

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

      5. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 0.1%

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

   6. Taylor expanded in m around inf 0.1%

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

      1. +-commutative 0.1%

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

      2. distribute-rgt-in 0.1%

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

      3. *-lft-identity 0.1%

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

      4. associate-+l+ 0.1%

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

      5. associate-/r/ 0.1%

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

      6. neg-mul-1 0.1%

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

      7. distribute-frac-neg 0.1%

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

      8. unpow2 0.1%

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

      9. distribute-rgt-neg-out 0.1%

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

      10. associate-*l/ 0.1%

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

      11. distribute-rgt-neg-out 0.1%

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

      12. associate-/r/ 0.1%

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

      13. sub-neg 0.1%

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

      14. div-sub 0.1%

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

      15. associate-/r/ 0.1%

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

      16. *-commutative 0.1%

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

   8. Simplified 0.1%

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

      1. *-commutative 0.1%

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

      2. distribute-rgt1-in 0.1%

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

      3. *-un-lft-identity 0.1%

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

      4. *-un-lft-identity 0.1%

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

      5. sub-neg 0.1%

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

      6. +-commutative 0.1%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 75.0%

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

      9. sqr-neg 75.0%

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

      10. sqrt-unprod 75.0%

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

      11. add-sqr-sqrt 75.0%

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

   10. Applied egg-rr 75.0%

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

4. Final simplification 86.2%

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

Alternative 6: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 7: 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%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in v around 0 99.9%

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

   1. associate-*l/ 100.0%

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

   2. associate-/r/ 99.9%

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

7. Simplified 99.9%

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

8. Final simplification 99.9%

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

Alternative 8: 75.7% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in m around 0 72.5%

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

   1. +-commutative 72.5%

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

   2. distribute-lft-in 72.5%

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

   3. div-inv 72.5%

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

   4. *-rgt-identity 72.5%

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

7. Applied egg-rr 72.5%

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

8. Final simplification 72.5%

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

Alternative 9: 26.9% 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%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in v around inf 26.4%

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

   1. neg-mul-1 26.4%

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

   2. neg-sub0 26.4%

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

   3. associate--r- 26.4%

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

   4. metadata-eval 26.4%

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

7. Simplified 26.4%

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

8. Final simplification 26.4%

   \[\leadsto m + -1 \]
9. Add Preprocessing

Alternative 10: 24.4% 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%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in m around 0 23.8%

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

6. Final simplification 23.8%

   \[\leadsto -1 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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)))