b parameter of renormalized beta distribution

Percentage Accurate: 99.9% → 99.8%

Time: 6.7s

Alternatives: 12

Speedup: N/A×

• 41.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.3 \cdot 10^{-14}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(1 - m\right) \cdot \left(m \cdot \left(1 - m\right)\right)}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.3e-14)
   (* (- 1.0 m) (+ -1.0 (/ m v)))
   (/ (* (- 1.0 m) (* m (- 1.0 m))) v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.3e-14) {
		tmp = (1.0 - m) * (-1.0 + (m / v));
	} else {
		tmp = ((1.0 - m) * (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 <= 1.3d-14) then
        tmp = (1.0d0 - m) * ((-1.0d0) + (m / v))
    else
        tmp = ((1.0d0 - m) * (m * (1.0d0 - m))) / v
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.3e-14) {
		tmp = (1.0 - m) * (-1.0 + (m / v));
	} else {
		tmp = ((1.0 - m) * (m * (1.0 - m))) / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.3e-14:
		tmp = (1.0 - m) * (-1.0 + (m / v))
	else:
		tmp = ((1.0 - m) * (m * (1.0 - m))) / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.3e-14)
		tmp = Float64(Float64(1.0 - m) * Float64(-1.0 + Float64(m / v)));
	else
		tmp = Float64(Float64(Float64(1.0 - m) * Float64(m * Float64(1.0 - m))) / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.3e-14)
		tmp = (1.0 - m) * (-1.0 + (m / v));
	else
		tmp = ((1.0 - m) * (m * (1.0 - m))) / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.3e-14], N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - m), $MachinePrecision] * N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.29999999999999998e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in m around 0 100.0%

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

   if 1.29999999999999998e-14 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. frac-2neg 99.9%

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

      2. div-inv 99.9%

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

      3. distribute-neg-frac 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. frac-2neg 99.9%

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

      2. div-inv 99.9%

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

      3. remove-double-neg 99.9%

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

      4. neg-mul-1 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. add-sqr-sqrt 0.0%

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

      9. sqrt-unprod 3.0%

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

      10. sqr-neg 3.0%

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

      11. sqrt-unprod 3.0%

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

      12. add-sqr-sqrt 3.0%

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

      13. neg-mul-1 3.0%

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

      14. add-sqr-sqrt 0.0%

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

      15. sqrt-unprod 99.9%

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

      16. sqr-neg 99.9%

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

      17. sqrt-unprod 99.8%

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

      18. add-sqr-sqrt 99.9%

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

   7. Applied egg-rr 99.9%

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

      1. associate-*r/ 99.9%

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

      2. *-rgt-identity 99.9%

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

      3. +-commutative 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in v around 0 99.9%

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

       1. mul-1-neg 99.9%

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

       2. sub-neg 99.9%

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

       3. metadata-eval 99.9%

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

       4. *-commutative 99.9%

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

   12. Simplified 99.9%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.3 \cdot 10^{-14}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(1 - m\right) \cdot \left(m \cdot \left(1 - m\right)\right)}{v}\\ \end{array} \]

Alternative 2: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 6 \cdot 10^{-15}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(m + -1\right) \cdot \left(\frac{m}{v} \cdot \left(m + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 6e-15)
   (* (- 1.0 m) (+ -1.0 (/ m v)))
   (* (+ m -1.0) (* (/ m v) (+ m -1.0)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 6e-15) {
		tmp = (1.0 - m) * (-1.0 + (m / v));
	} else {
		tmp = (m + -1.0) * ((m / v) * (m + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 6d-15) then
        tmp = (1.0d0 - m) * ((-1.0d0) + (m / v))
    else
        tmp = (m + (-1.0d0)) * ((m / v) * (m + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 6e-15) {
		tmp = (1.0 - m) * (-1.0 + (m / v));
	} else {
		tmp = (m + -1.0) * ((m / v) * (m + -1.0));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 6e-15:
		tmp = (1.0 - m) * (-1.0 + (m / v))
	else:
		tmp = (m + -1.0) * ((m / v) * (m + -1.0))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 6e-15)
		tmp = Float64(Float64(1.0 - m) * Float64(-1.0 + Float64(m / v)));
	else
		tmp = Float64(Float64(m + -1.0) * Float64(Float64(m / v) * Float64(m + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 6e-15)
		tmp = (1.0 - m) * (-1.0 + (m / v));
	else
		tmp = (m + -1.0) * ((m / v) * (m + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 6e-15], N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m + -1.0), $MachinePrecision] * N[(N[(m / v), $MachinePrecision] * N[(m + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 6e-15

   1. Initial program 100.0%

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

   2. Taylor expanded in m around 0 100.0%

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

   if 6e-15 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. frac-2neg 99.9%

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

      2. div-inv 99.9%

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

      3. distribute-neg-frac 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in v around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.9%

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

   8. Simplified 99.9%

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

      1. div-inv 99.9%

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

      2. unpow2 99.9%

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

      3. clear-num 99.8%

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

      4. associate-*l* 99.9%

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

   10. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 6 \cdot 10^{-15}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(m + -1\right) \cdot \left(\frac{m}{v} \cdot \left(m + -1\right)\right)\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-/l* 100.0%

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

   4. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-/l* 100.0%

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

   4. metadata-eval 100.0%

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

3. Simplified 100.0%

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

   1. clear-num 99.8%

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

   2. associate-/r/ 99.8%

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

   3. clear-num 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 5: 97.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 98.4%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. frac-2neg 99.9%

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

      2. div-inv 99.9%

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

      3. distribute-neg-frac 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in v around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in m around inf 98.3%

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

       1. unpow2 98.3%

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

   11. Simplified 98.3%

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

4. Final simplification 98.4%

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

Alternative 6: 98.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.65:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(m + -2\right)}{\frac{v}{m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.65) (* (- 1.0 m) (+ -1.0 (/ m v))) (/ (* m (+ m -2.0)) (/ v m))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.65) {
		tmp = (1.0 - m) * (-1.0 + (m / v));
	} else {
		tmp = (m * (m + -2.0)) / (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 <= 1.65d0) then
        tmp = (1.0d0 - m) * ((-1.0d0) + (m / v))
    else
        tmp = (m * (m + (-2.0d0))) / (v / m)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.65) {
		tmp = (1.0 - m) * (-1.0 + (m / v));
	} else {
		tmp = (m * (m + -2.0)) / (v / m);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.65:
		tmp = (1.0 - m) * (-1.0 + (m / v))
	else:
		tmp = (m * (m + -2.0)) / (v / m)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.65)
		tmp = Float64(Float64(1.0 - m) * Float64(-1.0 + Float64(m / v)));
	else
		tmp = Float64(Float64(m * Float64(m + -2.0)) / Float64(v / m));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.65)
		tmp = (1.0 - m) * (-1.0 + (m / v));
	else
		tmp = (m * (m + -2.0)) / (v / m);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.65], N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m * N[(m + -2.0), $MachinePrecision]), $MachinePrecision] / N[(v / m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.6499999999999999

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 98.4%

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

   if 1.6499999999999999 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. frac-2neg 99.9%

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

      2. div-inv 99.9%

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

      3. distribute-neg-frac 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in v around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in m around inf 99.0%

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

       1. unpow2 99.0%

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

       2. distribute-rgt-out 99.0%

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

   11. Simplified 99.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.65:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot \left(m + -2\right)}{\frac{v}{m}}\\ \end{array} \]

Alternative 7: 74.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 8.8 \cdot 10^{-199}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 2.25:\\ \;\;\;\;\frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 8.8e-199) -1.0 (if (<= m 2.25) (/ m v) (* m (/ m v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 8.8e-199) {
		tmp = -1.0;
	} else if (m <= 2.25) {
		tmp = m / v;
	} 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 <= 8.8d-199) then
        tmp = -1.0d0
    else if (m <= 2.25d0) then
        tmp = m / v
    else
        tmp = m * (m / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 8.8e-199) {
		tmp = -1.0;
	} else if (m <= 2.25) {
		tmp = m / v;
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 8.8e-199:
		tmp = -1.0
	elif m <= 2.25:
		tmp = m / v
	else:
		tmp = m * (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 8.8e-199)
		tmp = -1.0;
	elseif (m <= 2.25)
		tmp = Float64(m / v);
	else
		tmp = Float64(m * Float64(m / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 8.8e-199)
		tmp = -1.0;
	elseif (m <= 2.25)
		tmp = m / v;
	else
		tmp = m * (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 8.8e-199], -1.0, If[LessEqual[m, 2.25], N[(m / v), $MachinePrecision], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 8.7999999999999994e-199

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 81.0%

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

   if 8.7999999999999994e-199 < m < 2.25

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. frac-2neg 99.9%

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

      2. div-inv 99.5%

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

      3. distribute-neg-frac 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in v around 0 76.6%

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

      1. *-commutative 76.6%

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

      2. associate-/l* 76.3%

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

   8. Simplified 76.3%

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

   9. Taylor expanded in m around 0 73.9%

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

   if 2.25 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. distribute-rgt-in 0.1%

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

      3. *-un-lft-identity 0.1%

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

      4. sub-neg 0.1%

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

      5. metadata-eval 0.1%

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

      6. add-sqr-sqrt 0.0%

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

      7. sqrt-unprod 73.8%

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

      8. sqr-neg 73.8%

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

      9. sqrt-unprod 73.8%

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

      10. add-sqr-sqrt 73.8%

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

      11. sub-neg 73.8%

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

      12. metadata-eval 73.8%

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

   4. Applied egg-rr 73.8%

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

      1. distribute-rgt1-in 73.8%

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

   6. Simplified 73.8%

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

   7. Taylor expanded in m around inf 73.8%

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

      1. unpow2 73.8%

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

      2. associate-*r/ 73.8%

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

   9. Simplified 73.8%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 8.8 \cdot 10^{-199}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 2.25:\\ \;\;\;\;\frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]

Alternative 8: 88.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.25:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.25) (+ -1.0 (+ m (/ m v))) (* m (/ m v))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.25) {
		tmp = -1.0 + (m + (m / v));
	} 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 <= 2.25d0) then
        tmp = (-1.0d0) + (m + (m / v))
    else
        tmp = m * (m / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 2.25) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = m * (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.25:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = m * (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.25)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(m * Float64(m / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.25)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = m * (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.25], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.25

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 98.1%

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

      1. sub-neg 98.1%

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

      2. metadata-eval 98.1%

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

      3. +-commutative 98.1%

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

      4. *-commutative 98.1%

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

      5. distribute-rgt-in 98.1%

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

      6. *-lft-identity 98.1%

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

      7. associate-*l/ 98.4%

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

      8. *-lft-identity 98.4%

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

   6. Simplified 98.4%

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

   if 2.25 < m

   1. Initial program 99.9%

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

   2. Taylor expanded in m around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. distribute-rgt-in 0.1%

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

      3. *-un-lft-identity 0.1%

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

      4. sub-neg 0.1%

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

      5. metadata-eval 0.1%

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

      6. add-sqr-sqrt 0.0%

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

      7. sqrt-unprod 73.8%

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

      8. sqr-neg 73.8%

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

      9. sqrt-unprod 73.8%

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

      10. add-sqr-sqrt 73.8%

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

      11. sub-neg 73.8%

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

      12. metadata-eval 73.8%

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

   4. Applied egg-rr 73.8%

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

      1. distribute-rgt1-in 73.8%

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

   6. Simplified 73.8%

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

   7. Taylor expanded in m around inf 73.8%

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

      1. unpow2 73.8%

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

      2. associate-*r/ 73.8%

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

   9. Simplified 73.8%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.25:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{v}\\ \end{array} \]

Alternative 9: 97.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.6:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot m}{\frac{v}{m}}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.6) (+ -1.0 (+ m (/ m v))) (/ (* m m) (/ v m))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.6) {
		tmp = -1.0 + (m + (m / v));
	} 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 <= 2.6d0) then
        tmp = (-1.0d0) + (m + (m / v))
    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 <= 2.6) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m * m) / (v / m);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.6:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = (m * m) / (v / m)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.6)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(Float64(m * m) / Float64(v / m));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.6)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = (m * m) / (v / m);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.6], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m * m), $MachinePrecision] / N[(v / m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.60000000000000009

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 98.1%

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

      1. sub-neg 98.1%

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

      2. metadata-eval 98.1%

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

      3. +-commutative 98.1%

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

      4. *-commutative 98.1%

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

      5. distribute-rgt-in 98.1%

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

      6. *-lft-identity 98.1%

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

      7. associate-*l/ 98.4%

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

      8. *-lft-identity 98.4%

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

   6. Simplified 98.4%

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

   if 2.60000000000000009 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. frac-2neg 99.9%

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

      2. div-inv 99.9%

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

      3. distribute-neg-frac 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in v around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in m around inf 98.3%

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

       1. unpow2 98.3%

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

   11. Simplified 98.3%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.6:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m \cdot m}{\frac{v}{m}}\\ \end{array} \]

Alternative 10: 62.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 5.2 \cdot 10^{-199}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= m 5.2e-199) -1.0 (/ m v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 5.2e-199) {
		tmp = -1.0;
	} else {
		tmp = 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 <= 5.2d-199) then
        tmp = -1.0d0
    else
        tmp = m / v
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 5.2e-199) {
		tmp = -1.0;
	} else {
		tmp = m / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 5.2e-199:
		tmp = -1.0
	else:
		tmp = m / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 5.2e-199)
		tmp = -1.0;
	else
		tmp = Float64(m / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 5.2e-199)
		tmp = -1.0;
	else
		tmp = m / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 5.2e-199], -1.0, N[(m / v), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 5.2000000000000001e-199

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 81.0%

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

   if 5.2000000000000001e-199 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. frac-2neg 99.9%

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

      2. div-inv 99.8%

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

      3. distribute-neg-frac 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in v around 0 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-/l* 90.4%

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

   8. Simplified 90.4%

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

   9. Taylor expanded in m around 0 62.1%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 5.2 \cdot 10^{-199}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v}\\ \end{array} \]

Alternative 11: 27.6% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-/l* 100.0%

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

   4. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in v around inf 25.5%

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

   1. neg-mul-1 25.5%

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

   2. neg-sub0 25.5%

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

   3. associate--r- 25.5%

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

   4. metadata-eval 25.5%

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

6. Simplified 25.5%

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

7. Final simplification 25.5%

   \[\leadsto m + -1 \]

Alternative 12: 25.2% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(m, v):
	return -1.0

Julia

function code(m, v)
	return -1.0
end

MATLAB

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

Wolfram

code[m_, v_] := -1.0

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-/l* 100.0%

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

   4. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in m around 0 23.3%

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

5. Final simplification 23.3%

   \[\leadsto -1 \]

Reproduce

herbie shell --seed 2023224 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (and (< 0.0 m) (< 0.0 v)) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))