a parameter of renormalized beta distribution

Percentage Accurate: 99.8% → 99.8%

Time: 5.3s

Alternatives: 6

Speedup: 1.0×

• 41.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-*l/ 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

   1. sub-neg 99.9%

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

   2. distribute-lft-in 71.7%

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

   3. *-commutative 71.7%

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

   4. *-un-lft-identity 71.7%

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

5. Applied egg-rr 71.7%

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

6. Taylor expanded in v around -inf 94.4%

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

   1. mul-1-neg 94.4%

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

   2. mul-1-neg 94.4%

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

   3. unsub-neg 94.4%

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

   4. associate-/l* 99.8%

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

   5. associate-/r/ 99.9%

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

   6. mul-1-neg 99.9%

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

   7. +-commutative 99.9%

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

   8. unpow2 99.9%

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

   9. mul-1-neg 99.9%

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

   10. distribute-rgt-out 99.9%

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

8. Simplified 99.9%

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

9. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

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(m * Float64(-1.0 + Float64(Float64(m / v) * Float64(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[(m * N[(-1.0 + N[(N[(m / v), $MachinePrecision] * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-*l/ 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 4: 87.2% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.8%

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

   2. Taylor expanded in m around 0 98.0%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around 0 0.1%

      \[\leadsto \color{blue}{-1 \cdot m + \frac{{m}^{2}}{v}} \]
   5. Step-by-step derivation

      1. unpow2 0.1%

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

      2. associate-/l* 0.1%

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

      3. associate-/r/ 0.1%

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

   6. Applied egg-rr 0.1%

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

      1. fma-def 0.1%

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

      2. add-sqr-sqrt 0.1%

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

      3. sqrt-unprod 0.1%

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

      4. sqr-neg 0.1%

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

      5. distribute-rgt-neg-out 0.1%

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

      6. distribute-rgt-neg-out 0.1%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 75.5%

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

      9. distribute-rgt-neg-out 75.5%

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

      10. fma-neg 75.5%

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

      11. distribute-rgt-out-- 75.5%

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

   8. Applied egg-rr 75.5%

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

4. Final simplification 85.9%

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

Alternative 5: 62.7% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-*l/ 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in m around 0 40.2%

   \[\leadsto \color{blue}{-1 \cdot m + \frac{{m}^{2}}{v}} \]
5. Step-by-step derivation

   1. unpow2 40.2%

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

   2. associate-/l* 45.6%

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

   3. associate-/r/ 45.6%

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

6. Applied egg-rr 45.6%

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

   1. fma-def 45.6%

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

   2. add-sqr-sqrt 45.5%

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

   3. sqrt-unprod 40.2%

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

   4. sqr-neg 40.2%

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

   5. distribute-rgt-neg-out 40.2%

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

   6. distribute-rgt-neg-out 40.2%

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

   7. sqrt-unprod 12.1%

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

   8. add-sqr-sqrt 64.2%

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

   9. distribute-rgt-neg-out 64.2%

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

   10. fma-neg 64.2%

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

   11. distribute-rgt-out-- 64.2%

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

8. Applied egg-rr 64.2%

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

9. Final simplification 64.2%

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

Alternative 6: 26.9% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	return -m

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-*l/ 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in m around 0 27.0%

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

   1. neg-mul-1 27.0%

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

6. Simplified 27.0%

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

7. Final simplification 27.0%

   \[\leadsto -m \]

Reproduce

herbie shell --seed 2023318 
(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))