a parameter of renormalized beta distribution

Percentage Accurate: 99.9% → 99.9%

Time: 5.9s

Alternatives: 7

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

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

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: 99.9% 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: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-*l/ 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 75.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 3.2 \cdot 10^{-175}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(-1 - \frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 3.2e-175)
   (- m)
   (if (<= m 1.0) (/ m (/ v m)) (* m (- -1.0 (/ m v))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 3.2e-175) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} 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 <= 3.2d-175) then
        tmp = -m
    else if (m <= 1.0d0) then
        tmp = m / (v / m)
    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 <= 3.2e-175) {
		tmp = -m;
	} else if (m <= 1.0) {
		tmp = m / (v / m);
	} else {
		tmp = m * (-1.0 - (m / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 3.2e-175:
		tmp = -m
	elif m <= 1.0:
		tmp = m / (v / m)
	else:
		tmp = m * (-1.0 - (m / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 3.2e-175)
		tmp = Float64(-m);
	elseif (m <= 1.0)
		tmp = Float64(m / Float64(v / m));
	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 <= 3.2e-175)
		tmp = -m;
	elseif (m <= 1.0)
		tmp = m / (v / m);
	else
		tmp = m * (-1.0 - (m / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 3.2e-175], (-m), If[LessEqual[m, 1.0], N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision], N[(m * N[(-1.0 - N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 3.2e-175

   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 76.7%

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

      1. neg-mul-1 76.7%

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

   6. Simplified 76.7%

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

   if 3.2e-175 < m < 1

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l/ 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in m around 0 94.4%

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

   5. Taylor expanded in m around inf 73.0%

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

      1. clear-num 72.9%

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

      2. un-div-inv 73.0%

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

   7. Applied egg-rr 73.0%

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

   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%

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

      1. div-inv 0.1%

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

      2. fma-neg 0.1%

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

      3. metadata-eval 0.1%

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

      4. frac-2neg 0.1%

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

      5. metadata-eval 0.1%

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

      6. add-sqr-sqrt 0.0%

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

      7. sqrt-unprod 81.1%

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

      8. sqr-neg 81.1%

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

      9. sqrt-unprod 79.7%

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

      10. add-sqr-sqrt 79.7%

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

   6. Applied egg-rr 79.7%

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

      1. fma-udef 79.7%

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

      2. associate-*r/ 79.7%

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

      3. associate-*l/ 79.7%

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

      4. metadata-eval 79.7%

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

      5. distribute-rgt-in 79.7%

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

      6. neg-mul-1 79.7%

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

      7. neg-sub0 79.7%

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

      8. +-commutative 79.7%

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

      9. associate--r+ 79.7%

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

      10. metadata-eval 79.7%

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

   8. Simplified 79.7%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 3.2 \cdot 10^{-175}:\\ \;\;\;\;-m\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(-1 - \frac{m}{v}\right)\\ \end{array} \]

Alternative 3: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 8.6 \cdot 10^{-12}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} \cdot \left(1 - m\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 8.6e-12) (* m (+ (/ m v) -1.0)) (* m (* (/ m v) (- 1.0 m)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 8.6e-12) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = m * ((m / v) * (1.0 - m));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 8.6d-12) then
        tmp = m * ((m / v) + (-1.0d0))
    else
        tmp = m * ((m / v) * (1.0d0 - m))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 8.6e-12) {
		tmp = m * ((m / v) + -1.0);
	} else {
		tmp = m * ((m / v) * (1.0 - m));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 8.6e-12:
		tmp = m * ((m / v) + -1.0)
	else:
		tmp = m * ((m / v) * (1.0 - m))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 8.6e-12)
		tmp = Float64(m * Float64(Float64(m / v) + -1.0));
	else
		tmp = Float64(m * Float64(Float64(m / v) * Float64(1.0 - m)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 8.6e-12)
		tmp = m * ((m / v) + -1.0);
	else
		tmp = m * ((m / v) * (1.0 - m));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 8.6e-12], N[(m * N[(N[(m / v), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(m * N[(N[(m / v), $MachinePrecision] * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 8.59999999999999971e-12

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l/ 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in m around 0 99.5%

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

   if 8.59999999999999971e-12 < 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. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in v around 0 99.9%

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

      1. associate-/l* 99.9%

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

   8. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. unpow2 99.9%

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

      3. associate-*r/ 99.9%

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

      4. associate-*l* 99.9%

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

   10. Applied egg-rr 99.9%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 8.6 \cdot 10^{-12}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} \cdot \left(1 - m\right)\right)\\ \end{array} \]

Alternative 4: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 9.2 \cdot 10^{-179} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (or (<= m 9.2e-179) (not (<= m 1.0))) (- m) (* m (/ m v))))

C

double code(double m, double v) {
	double tmp;
	if ((m <= 9.2e-179) || !(m <= 1.0)) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if ((m <= 9.2d-179) .or. (.not. (m <= 1.0d0))) then
        tmp = -m
    else
        tmp = m * (m / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if ((m <= 9.2e-179) || !(m <= 1.0)) {
		tmp = -m;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (m <= 9.2e-179) or not (m <= 1.0):
		tmp = -m
	else:
		tmp = m * (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if ((m <= 9.2e-179) || !(m <= 1.0))
		tmp = Float64(-m);
	else
		tmp = Float64(m * Float64(m / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if ((m <= 9.2e-179) || ~((m <= 1.0)))
		tmp = -m;
	else
		tmp = m * (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[Or[LessEqual[m, 9.2e-179], N[Not[LessEqual[m, 1.0]], $MachinePrecision]], (-m), N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 9.1999999999999995e-179 or 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 28.7%

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

      1. neg-mul-1 28.7%

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

   6. Simplified 28.7%

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

   if 9.1999999999999995e-179 < m < 1

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l/ 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in m around 0 94.4%

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

   5. Taylor expanded in m around inf 73.0%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 9.2 \cdot 10^{-179} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]

Alternative 5: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 7.5 \cdot 10^{-177} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (or (<= m 7.5e-177) (not (<= m 1.0))) (- m) (/ m (/ v m))))

C

double code(double m, double v) {
	double tmp;
	if ((m <= 7.5e-177) || !(m <= 1.0)) {
		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 <= 7.5d-177) .or. (.not. (m <= 1.0d0))) 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 <= 7.5e-177) || !(m <= 1.0)) {
		tmp = -m;
	} else {
		tmp = m / (v / m);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if (m <= 7.5e-177) or not (m <= 1.0):
		tmp = -m
	else:
		tmp = m / (v / m)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if ((m <= 7.5e-177) || !(m <= 1.0))
		tmp = Float64(-m);
	else
		tmp = Float64(m / Float64(v / m));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if ((m <= 7.5e-177) || ~((m <= 1.0)))
		tmp = -m;
	else
		tmp = m / (v / m);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[Or[LessEqual[m, 7.5e-177], N[Not[LessEqual[m, 1.0]], $MachinePrecision]], (-m), N[(m / N[(v / m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 7.5e-177 or 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 28.7%

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

      1. neg-mul-1 28.7%

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

   6. Simplified 28.7%

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

   if 7.5e-177 < m < 1

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l/ 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in m around 0 94.4%

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

   5. Taylor expanded in m around inf 73.0%

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

      1. clear-num 72.9%

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

      2. un-div-inv 73.0%

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

   7. Applied egg-rr 73.0%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 7.5 \cdot 10^{-177} \lor \neg \left(m \leq 1\right):\\ \;\;\;\;-m\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{\frac{v}{m}}\\ \end{array} \]

Alternative 6: 87.7% 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 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l/ 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in m around 0 96.9%

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

   if 1 < m

   1. Initial program 99.9%

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

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

      1. div-inv 0.1%

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

      2. fma-neg 0.1%

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

      3. metadata-eval 0.1%

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

      4. frac-2neg 0.1%

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

      5. metadata-eval 0.1%

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

      6. add-sqr-sqrt 0.0%

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

      7. sqrt-unprod 81.1%

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

      8. sqr-neg 81.1%

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

      9. sqrt-unprod 79.7%

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

      10. add-sqr-sqrt 79.7%

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

   6. Applied egg-rr 79.7%

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

      1. fma-udef 79.7%

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

      2. associate-*r/ 79.7%

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

      3. associate-*l/ 79.7%

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

      4. metadata-eval 79.7%

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

      5. distribute-rgt-in 79.7%

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

      6. neg-mul-1 79.7%

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

      7. neg-sub0 79.7%

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

      8. +-commutative 79.7%

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

      9. associate--r+ 79.7%

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

      10. metadata-eval 79.7%

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

   8. Simplified 79.7%

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

4. Final simplification 88.5%

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

Alternative 7: 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 99.8%

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

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-*l/ 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in m around 0 25.7%

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

   1. neg-mul-1 25.7%

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

6. Simplified 25.7%

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

7. Final simplification 25.7%

   \[\leadsto -m \]

Reproduce

herbie shell --seed 2023298 
(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))