a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 6.6s

Alternatives: 10

Speedup: 1.0×

• 42.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

Alternative 2: 48.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \leq -1 \cdot 10^{-303}:\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= (* (- (/ (* m (- 1.0 m)) v) 1.0) m) -1e-303) (- m) (* (/ m v) m)))

C

double code(double m, double v) {
	double tmp;
	if (((((m * (1.0 - m)) / v) - 1.0) * m) <= -1e-303) {
		tmp = -m;
	} else {
		tmp = (m / v) * m;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (((((m * (1.0d0 - m)) / v) - 1.0d0) * m) <= (-1d-303)) then
        tmp = -m
    else
        tmp = (m / v) * m
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (((((m * (1.0 - m)) / v) - 1.0) * m) <= -1e-303) {
		tmp = -m;
	} else {
		tmp = (m / v) * m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if ((((m * (1.0 - m)) / v) - 1.0) * m) <= -1e-303:
		tmp = -m
	else:
		tmp = (m / v) * m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(m * Float64(1.0 - m)) / v) - 1.0) * m) <= -1e-303)
		tmp = Float64(-m);
	else
		tmp = Float64(Float64(m / v) * m);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (((((m * (1.0 - m)) / v) - 1.0) * m) <= -1e-303)
		tmp = -m;
	else
		tmp = (m / v) * m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[N[(N[(N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision] - 1.0), $MachinePrecision] * m), $MachinePrecision], -1e-303], (-m), N[(N[(m / v), $MachinePrecision] * m), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m) < -9.99999999999999931e-304

   1. Initial program 100.0%

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

   3. Taylor expanded in m around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(m\right)} \]

      2. lower-neg.f64 32.3

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

   5. Applied rewrites 32.3%

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

   if -9.99999999999999931e-304 < (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 #s(literal 1 binary64) m)) v) #s(literal 1 binary64)) m)

   1. Initial program 99.4%

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

   3. Taylor expanded in m around inf

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

      1. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{\frac{1}{m \cdot v} \cdot {m}^{3} - \frac{1}{v} \cdot {m}^{3}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{{m}^{3} \cdot \frac{1}{m \cdot v}} - \frac{1}{v} \cdot {m}^{3} \]

      3. unpow3 N/A

         \[\leadsto \color{blue}{\left(\left(m \cdot m\right) \cdot m\right)} \cdot \frac{1}{m \cdot v} - \frac{1}{v} \cdot {m}^{3} \]

      4. unpow2 N/A

         \[\leadsto \left(\color{blue}{{m}^{2}} \cdot m\right) \cdot \frac{1}{m \cdot v} - \frac{1}{v} \cdot {m}^{3} \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{{m}^{2} \cdot \left(m \cdot \frac{1}{m \cdot v}\right)} - \frac{1}{v} \cdot {m}^{3} \]

      6. associate-/r* N/A

         \[\leadsto {m}^{2} \cdot \left(m \cdot \color{blue}{\frac{\frac{1}{m}}{v}}\right) - \frac{1}{v} \cdot {m}^{3} \]

      7. associate-*r/ N/A

         \[\leadsto {m}^{2} \cdot \color{blue}{\frac{m \cdot \frac{1}{m}}{v}} - \frac{1}{v} \cdot {m}^{3} \]

      8. rgt-mult-inverse N/A

         \[\leadsto {m}^{2} \cdot \frac{\color{blue}{1}}{v} - \frac{1}{v} \cdot {m}^{3} \]

      9. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{{m}^{2} \cdot 1}{v}} - \frac{1}{v} \cdot {m}^{3} \]

      10. *-rgt-identity N/A

          \[\leadsto \frac{\color{blue}{{m}^{2}}}{v} - \frac{1}{v} \cdot {m}^{3} \]

      11. unpow2 N/A

          \[\leadsto \frac{\color{blue}{m \cdot m}}{v} - \frac{1}{v} \cdot {m}^{3} \]

      12. associate-*l/ N/A

          \[\leadsto \color{blue}{\frac{m}{v} \cdot m} - \frac{1}{v} \cdot {m}^{3} \]

      13. cube-mult N/A

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

      14. unpow2 N/A

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

      15. associate-*r* N/A

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

      16. associate-*l/ N/A

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

      17. *-lft-identity N/A

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in m around 0

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

   8. Applied rewrites 91.5%

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

Alternative 3: 99.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.75 \cdot 10^{-22}:\\ \;\;\;\;\left(\frac{m}{v} - 1\right) \cdot m\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \frac{m \cdot m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.75e-22) (* (- (/ m v) 1.0) m) (* (- 1.0 m) (/ (* m m) v))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.75e-22) {
		tmp = ((m / v) - 1.0) * m;
	} else {
		tmp = (1.0 - m) * ((m * m) / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.75d-22) then
        tmp = ((m / v) - 1.0d0) * m
    else
        tmp = (1.0d0 - m) * ((m * m) / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.75e-22) {
		tmp = ((m / v) - 1.0) * m;
	} else {
		tmp = (1.0 - m) * ((m * m) / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.75e-22:
		tmp = ((m / v) - 1.0) * m
	else:
		tmp = (1.0 - m) * ((m * m) / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.75e-22)
		tmp = Float64(Float64(Float64(m / v) - 1.0) * m);
	else
		tmp = Float64(Float64(1.0 - m) * Float64(Float64(m * m) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.75e-22)
		tmp = ((m / v) - 1.0) * m;
	else
		tmp = (1.0 - m) * ((m * m) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.75e-22], N[(N[(N[(m / v), $MachinePrecision] - 1.0), $MachinePrecision] * m), $MachinePrecision], N[(N[(1.0 - m), $MachinePrecision] * N[(N[(m * m), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.75000000000000003e-22

   1. Initial program 99.7%

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

   3. Taylor expanded in m around 0

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

      1. lower-/.f64 99.7

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

   5. Applied rewrites 99.7%

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

   if 1.75000000000000003e-22 < m

   1. Initial program 99.9%

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

   3. Taylor expanded in m around inf

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

      1. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{\frac{1}{m \cdot v} \cdot {m}^{3} - \frac{1}{v} \cdot {m}^{3}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{{m}^{3} \cdot \frac{1}{m \cdot v}} - \frac{1}{v} \cdot {m}^{3} \]

      3. unpow3 N/A

         \[\leadsto \color{blue}{\left(\left(m \cdot m\right) \cdot m\right)} \cdot \frac{1}{m \cdot v} - \frac{1}{v} \cdot {m}^{3} \]

      4. unpow2 N/A

         \[\leadsto \left(\color{blue}{{m}^{2}} \cdot m\right) \cdot \frac{1}{m \cdot v} - \frac{1}{v} \cdot {m}^{3} \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{{m}^{2} \cdot \left(m \cdot \frac{1}{m \cdot v}\right)} - \frac{1}{v} \cdot {m}^{3} \]

      6. associate-/r* N/A

         \[\leadsto {m}^{2} \cdot \left(m \cdot \color{blue}{\frac{\frac{1}{m}}{v}}\right) - \frac{1}{v} \cdot {m}^{3} \]

      7. associate-*r/ N/A

         \[\leadsto {m}^{2} \cdot \color{blue}{\frac{m \cdot \frac{1}{m}}{v}} - \frac{1}{v} \cdot {m}^{3} \]

      8. rgt-mult-inverse N/A

         \[\leadsto {m}^{2} \cdot \frac{\color{blue}{1}}{v} - \frac{1}{v} \cdot {m}^{3} \]

      9. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{{m}^{2} \cdot 1}{v}} - \frac{1}{v} \cdot {m}^{3} \]

      10. *-rgt-identity N/A

          \[\leadsto \frac{\color{blue}{{m}^{2}}}{v} - \frac{1}{v} \cdot {m}^{3} \]

      11. unpow2 N/A

          \[\leadsto \frac{\color{blue}{m \cdot m}}{v} - \frac{1}{v} \cdot {m}^{3} \]

      12. associate-*l/ N/A

          \[\leadsto \color{blue}{\frac{m}{v} \cdot m} - \frac{1}{v} \cdot {m}^{3} \]

      13. cube-mult N/A

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

      14. unpow2 N/A

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

      15. associate-*r* N/A

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

      16. associate-*l/ N/A

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

      17. *-lft-identity N/A

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

   5. Applied rewrites 99.9%

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

   7. Applied rewrites 99.9%

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

Alternative 4: 97.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in m around 0

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

      1. lower-/.f64 97.7

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

   5. Applied rewrites 97.7%

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

   if 1 < m

   1. Initial program 100.0%

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

   3. Taylor expanded in m around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. unpow2 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 97.5

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

   5. Applied rewrites 97.5%

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

4. Final simplification 97.6%

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

Alternative 5: 97.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in m around 0

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

      1. lower-/.f64 97.7

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

   5. Applied rewrites 97.7%

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

   if 1 < m

   1. Initial program 100.0%

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

   3. Taylor expanded in m around inf

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

      1. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{\frac{1}{m \cdot v} \cdot {m}^{3} - \frac{1}{v} \cdot {m}^{3}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{{m}^{3} \cdot \frac{1}{m \cdot v}} - \frac{1}{v} \cdot {m}^{3} \]

      3. unpow3 N/A

         \[\leadsto \color{blue}{\left(\left(m \cdot m\right) \cdot m\right)} \cdot \frac{1}{m \cdot v} - \frac{1}{v} \cdot {m}^{3} \]

      4. unpow2 N/A

         \[\leadsto \left(\color{blue}{{m}^{2}} \cdot m\right) \cdot \frac{1}{m \cdot v} - \frac{1}{v} \cdot {m}^{3} \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{{m}^{2} \cdot \left(m \cdot \frac{1}{m \cdot v}\right)} - \frac{1}{v} \cdot {m}^{3} \]

      6. associate-/r* N/A

         \[\leadsto {m}^{2} \cdot \left(m \cdot \color{blue}{\frac{\frac{1}{m}}{v}}\right) - \frac{1}{v} \cdot {m}^{3} \]

      7. associate-*r/ N/A

         \[\leadsto {m}^{2} \cdot \color{blue}{\frac{m \cdot \frac{1}{m}}{v}} - \frac{1}{v} \cdot {m}^{3} \]

      8. rgt-mult-inverse N/A

         \[\leadsto {m}^{2} \cdot \frac{\color{blue}{1}}{v} - \frac{1}{v} \cdot {m}^{3} \]

      9. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{{m}^{2} \cdot 1}{v}} - \frac{1}{v} \cdot {m}^{3} \]

      10. *-rgt-identity N/A

          \[\leadsto \frac{\color{blue}{{m}^{2}}}{v} - \frac{1}{v} \cdot {m}^{3} \]

      11. unpow2 N/A

          \[\leadsto \frac{\color{blue}{m \cdot m}}{v} - \frac{1}{v} \cdot {m}^{3} \]

      12. associate-*l/ N/A

          \[\leadsto \color{blue}{\frac{m}{v} \cdot m} - \frac{1}{v} \cdot {m}^{3} \]

      13. cube-mult N/A

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

      14. unpow2 N/A

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

      15. associate-*r* N/A

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

      16. associate-*l/ N/A

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

      17. *-lft-identity N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in m around inf

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

   8. Applied rewrites 97.5%

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

Alternative 6: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift-/.f64 N/A

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

   2. clear-num N/A

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

   3. lower-/.f64 N/A

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

   4. lower-/.f64 99.8

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Taylor expanded in v around 0

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

   1. lower-/.f64 N/A

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

   2. +-commutative N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 N/A

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

   5. lower--.f64 N/A

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

   6. mul-1-neg N/A

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

   7. lower-neg.f64 99.8

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

7. Applied rewrites 99.8%

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

Alternative 7: 74.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in m around 0

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

      1. lower-/.f64 97.7

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

   5. Applied rewrites 97.7%

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

   if 1 < m

   1. Initial program 100.0%

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

   3. Taylor expanded in m around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(m\right)} \]

      2. lower-neg.f64 5.5

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

   5. Applied rewrites 5.5%

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

   7. Applied rewrites 51.4%

      \[\leadsto \frac{0 - m \cdot m}{\color{blue}{0 + m}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.9%

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

Alternative 8: 50.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in m around 0

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

      1. lower-/.f64 97.7

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

   5. Applied rewrites 97.7%

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

   if 1 < m

   1. Initial program 100.0%

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

   3. Taylor expanded in m around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(m\right)} \]

      2. lower-neg.f64 5.5

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

   5. Applied rewrites 5.5%

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

Alternative 9: 50.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.6%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 99.6

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in v around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 99.6

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

   7. Applied rewrites 99.6%

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

   8. Taylor expanded in m around 0

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

   10. Applied rewrites 97.7%

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

   if 1 < m

   1. Initial program 100.0%

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

   3. Taylor expanded in m around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(m\right)} \]

      2. lower-neg.f64 5.5

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

   5. Applied rewrites 5.5%

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

Alternative 10: 26.8% accurate, 9.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	return -m

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in m around 0

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(m\right)} \]

   2. lower-neg.f64 23.2

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

5. Applied rewrites 23.2%

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

Reproduce

herbie shell --seed 2024322 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (and (< 0.0 m) (< 0.0 v)) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))