b parameter of renormalized beta distribution

Percentage Accurate: 99.9% → 99.9%

Time: 8.3s

Alternatives: 13

Speedup: 1.0×

• 41.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 85.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 4.4 \cdot 10^{-136}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1.6:\\ \;\;\;\;\frac{m}{v} \cdot \left(\left(--1\right) - m\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m \cdot \left(m + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 4.4e-136)
   -1.0
   (if (<= m 1.6) (* (/ m v) (- (- -1.0) m)) (* (/ m v) (* m (+ m -2.0))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 4.4e-136) {
		tmp = -1.0;
	} else if (m <= 1.6) {
		tmp = (m / v) * (-(-1.0) - m);
	} else {
		tmp = (m / v) * (m * (m + -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 4.4d-136) then
        tmp = -1.0d0
    else if (m <= 1.6d0) then
        tmp = (m / v) * (-(-1.0d0) - m)
    else
        tmp = (m / v) * (m * (m + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 4.4e-136) {
		tmp = -1.0;
	} else if (m <= 1.6) {
		tmp = (m / v) * (-(-1.0) - m);
	} else {
		tmp = (m / v) * (m * (m + -2.0));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 4.4e-136:
		tmp = -1.0
	elif m <= 1.6:
		tmp = (m / v) * (-(-1.0) - m)
	else:
		tmp = (m / v) * (m * (m + -2.0))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 4.4e-136)
		tmp = -1.0;
	elseif (m <= 1.6)
		tmp = Float64(Float64(m / v) * Float64(Float64(-(-1.0)) - m));
	else
		tmp = Float64(Float64(m / v) * Float64(m * Float64(m + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 4.4e-136)
		tmp = -1.0;
	elseif (m <= 1.6)
		tmp = (m / v) * (-(-1.0) - m);
	else
		tmp = (m / v) * (m * (m + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 4.4e-136], -1.0, If[LessEqual[m, 1.6], N[(N[(m / v), $MachinePrecision] * N[((--1.0) - m), $MachinePrecision]), $MachinePrecision], N[(N[(m / v), $MachinePrecision] * N[(m * N[(m + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 4.4000000000000002e-136

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 71.0%

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

   if 4.4000000000000002e-136 < m < 1.6000000000000001

   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* 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in m around 0 94.9%

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

      1. div-inv 95.2%

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

      2. add-sqr-sqrt 94.7%

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

      3. sqrt-unprod 95.2%

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

      4. sqr-neg 95.2%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 21.9%

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

      7. neg-mul-1 21.9%

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

      8. *-commutative 21.9%

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

      9. associate-*l/ 21.9%

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

      10. clear-num 21.9%

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

      11. associate-*l/ 21.9%

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

      12. metadata-eval 21.9%

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

   7. Applied egg-rr 21.9%

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

   8. Taylor expanded in v around 0 2.5%

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

      1. mul-1-neg 2.5%

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

      2. associate-/l* 2.5%

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

      3. distribute-rgt-neg-in 2.5%

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

      4. distribute-frac-neg 2.5%

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

      5. neg-sub0 2.5%

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

      6. associate--r- 2.5%

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

      7. metadata-eval 2.5%

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

      8. +-commutative 2.5%

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

   10. Simplified 2.5%

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

       1. associate-*r/ 2.5%

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

       2. add-sqr-sqrt 2.5%

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

       3. times-frac 2.5%

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

       4. +-commutative 2.5%

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

       5. metadata-eval 2.5%

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

       6. associate--r- 2.5%

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

       7. neg-sub0 2.5%

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

       8. times-frac 2.5%

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

       9. add-sqr-sqrt 2.5%

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

       10. div-inv 2.5%

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

       11. distribute-rgt-neg-out 2.5%

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

       12. remove-double-neg 2.5%

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

       13. distribute-rgt-neg-out 2.5%

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

       14. distribute-lft-neg-out 2.5%

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

   12. Applied egg-rr 71.7%

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

   if 1.6000000000000001 < m

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in m around inf 98.3%

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

      1. +-commutative 98.3%

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

      2. unpow2 98.3%

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

      3. distribute-rgt-out 98.3%

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

   10. Simplified 98.3%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 4.4 \cdot 10^{-136}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1.6:\\ \;\;\;\;\frac{m}{v} \cdot \left(\left(--1\right) - m\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m \cdot \left(m + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 9.4 \cdot 10^{-132}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{v} \cdot \left(1 + m \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m \cdot \left(m + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 9.4e-132)
   -1.0
   (if (<= m 1.0)
     (* (/ m v) (+ 1.0 (* m -2.0)))
     (* (/ m v) (* m (+ m -2.0))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 9.4e-132) {
		tmp = -1.0;
	} else if (m <= 1.0) {
		tmp = (m / v) * (1.0 + (m * -2.0));
	} else {
		tmp = (m / v) * (m * (m + -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 9.4d-132) then
        tmp = -1.0d0
    else if (m <= 1.0d0) then
        tmp = (m / v) * (1.0d0 + (m * (-2.0d0)))
    else
        tmp = (m / v) * (m * (m + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 9.4e-132) {
		tmp = -1.0;
	} else if (m <= 1.0) {
		tmp = (m / v) * (1.0 + (m * -2.0));
	} else {
		tmp = (m / v) * (m * (m + -2.0));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 9.4e-132:
		tmp = -1.0
	elif m <= 1.0:
		tmp = (m / v) * (1.0 + (m * -2.0))
	else:
		tmp = (m / v) * (m * (m + -2.0))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 9.4e-132)
		tmp = -1.0;
	elseif (m <= 1.0)
		tmp = Float64(Float64(m / v) * Float64(1.0 + Float64(m * -2.0)));
	else
		tmp = Float64(Float64(m / v) * Float64(m * Float64(m + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 9.4e-132)
		tmp = -1.0;
	elseif (m <= 1.0)
		tmp = (m / v) * (1.0 + (m * -2.0));
	else
		tmp = (m / v) * (m * (m + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 9.4e-132], -1.0, If[LessEqual[m, 1.0], N[(N[(m / v), $MachinePrecision] * N[(1.0 + N[(m * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m / v), $MachinePrecision] * N[(m * N[(m + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 9.4000000000000004e-132

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 71.0%

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

   if 9.4000000000000004e-132 < m < 1

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in v around 0 76.5%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in m around 0 74.0%

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

      1. *-commutative 74.0%

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

   10. Simplified 74.0%

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

   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. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in m around inf 98.3%

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

      1. +-commutative 98.3%

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

      2. unpow2 98.3%

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

      3. distribute-rgt-out 98.3%

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

   10. Simplified 98.3%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 9.4 \cdot 10^{-132}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{v} \cdot \left(1 + m \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m \cdot \left(m + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.65 \cdot 10^{-134}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{v} \cdot \left(\left(--1\right) - m\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m + -1}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.65e-134)
   -1.0
   (if (<= m 1.0) (* (/ m v) (- (- -1.0) m)) (* m (/ (+ m -1.0) v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.65e-134) {
		tmp = -1.0;
	} else if (m <= 1.0) {
		tmp = (m / v) * (-(-1.0) - m);
	} else {
		tmp = m * ((m + -1.0) / 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 <= 1.65d-134) then
        tmp = -1.0d0
    else if (m <= 1.0d0) then
        tmp = (m / v) * (-(-1.0d0) - m)
    else
        tmp = m * ((m + (-1.0d0)) / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.65e-134) {
		tmp = -1.0;
	} else if (m <= 1.0) {
		tmp = (m / v) * (-(-1.0) - m);
	} else {
		tmp = m * ((m + -1.0) / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.65e-134:
		tmp = -1.0
	elif m <= 1.0:
		tmp = (m / v) * (-(-1.0) - m)
	else:
		tmp = m * ((m + -1.0) / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.65e-134)
		tmp = -1.0;
	elseif (m <= 1.0)
		tmp = Float64(Float64(m / v) * Float64(Float64(-(-1.0)) - m));
	else
		tmp = Float64(m * Float64(Float64(m + -1.0) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.65e-134)
		tmp = -1.0;
	elseif (m <= 1.0)
		tmp = (m / v) * (-(-1.0) - m);
	else
		tmp = m * ((m + -1.0) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.65e-134], -1.0, If[LessEqual[m, 1.0], N[(N[(m / v), $MachinePrecision] * N[((--1.0) - m), $MachinePrecision]), $MachinePrecision], N[(m * N[(N[(m + -1.0), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 1.6500000000000001e-134

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 71.0%

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

   if 1.6500000000000001e-134 < m < 1

   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* 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in m around 0 94.9%

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

      1. div-inv 95.2%

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

      2. add-sqr-sqrt 94.7%

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

      3. sqrt-unprod 95.2%

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

      4. sqr-neg 95.2%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 21.9%

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

      7. neg-mul-1 21.9%

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

      8. *-commutative 21.9%

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

      9. associate-*l/ 21.9%

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

      10. clear-num 21.9%

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

      11. associate-*l/ 21.9%

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

      12. metadata-eval 21.9%

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

   7. Applied egg-rr 21.9%

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

   8. Taylor expanded in v around 0 2.5%

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

      1. mul-1-neg 2.5%

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

      2. associate-/l* 2.5%

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

      3. distribute-rgt-neg-in 2.5%

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

      4. distribute-frac-neg 2.5%

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

      5. neg-sub0 2.5%

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

      6. associate--r- 2.5%

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

      7. metadata-eval 2.5%

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

      8. +-commutative 2.5%

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

   10. Simplified 2.5%

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

       1. associate-*r/ 2.5%

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

       2. add-sqr-sqrt 2.5%

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

       3. times-frac 2.5%

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

       4. +-commutative 2.5%

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

       5. metadata-eval 2.5%

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

       6. associate--r- 2.5%

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

       7. neg-sub0 2.5%

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

       8. times-frac 2.5%

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

       9. add-sqr-sqrt 2.5%

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

       10. div-inv 2.5%

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

       11. distribute-rgt-neg-out 2.5%

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

       12. remove-double-neg 2.5%

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

       13. distribute-rgt-neg-out 2.5%

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

       14. distribute-lft-neg-out 2.5%

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

   12. Applied egg-rr 71.7%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 0.1%

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

      1. div-inv 0.1%

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

      2. add-sqr-sqrt 0.1%

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

      3. sqrt-unprod 0.1%

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

      4. sqr-neg 0.1%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 76.4%

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

      7. neg-mul-1 76.4%

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

      8. *-commutative 76.4%

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

      9. associate-*l/ 76.4%

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

      10. clear-num 76.4%

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

      11. associate-*l/ 76.4%

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

      12. metadata-eval 76.4%

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

   7. Applied egg-rr 76.4%

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

   8. Taylor expanded in v around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. associate-/l* 76.4%

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

      3. distribute-rgt-neg-in 76.4%

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

      4. distribute-frac-neg 76.4%

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

      5. neg-sub0 76.4%

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

      6. associate--r- 76.4%

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

      7. metadata-eval 76.4%

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

      8. +-commutative 76.4%

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

   10. Simplified 76.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.65 \cdot 10^{-134}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{v} \cdot \left(\left(--1\right) - m\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m + -1}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 5.8 \cdot 10^{-136}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m + -1}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 5.8e-136) -1.0 (if (<= m 1.0) (/ m v) (* m (/ (+ m -1.0) v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 5.8e-136) {
		tmp = -1.0;
	} else if (m <= 1.0) {
		tmp = m / v;
	} else {
		tmp = m * ((m + -1.0) / 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 <= 5.8d-136) then
        tmp = -1.0d0
    else if (m <= 1.0d0) then
        tmp = m / v
    else
        tmp = m * ((m + (-1.0d0)) / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 5.8e-136) {
		tmp = -1.0;
	} else if (m <= 1.0) {
		tmp = m / v;
	} else {
		tmp = m * ((m + -1.0) / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 5.8e-136:
		tmp = -1.0
	elif m <= 1.0:
		tmp = m / v
	else:
		tmp = m * ((m + -1.0) / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 5.8e-136)
		tmp = -1.0;
	elseif (m <= 1.0)
		tmp = Float64(m / v);
	else
		tmp = Float64(m * Float64(Float64(m + -1.0) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 5.8e-136)
		tmp = -1.0;
	elseif (m <= 1.0)
		tmp = m / v;
	else
		tmp = m * ((m + -1.0) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 5.8e-136], -1.0, If[LessEqual[m, 1.0], N[(m / v), $MachinePrecision], N[(m * N[(N[(m + -1.0), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if m < 5.79999999999999989e-136

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 71.0%

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

   if 5.79999999999999989e-136 < m < 1

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in v around 0 76.5%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in m around 0 76.5%

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

      1. +-commutative 76.5%

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

      2. unpow2 76.5%

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

      3. distribute-rgt-out 76.5%

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

   10. Simplified 76.5%

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

   11. Taylor expanded in m around 0 71.5%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 0.1%

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

      1. div-inv 0.1%

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

      2. add-sqr-sqrt 0.1%

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

      3. sqrt-unprod 0.1%

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

      4. sqr-neg 0.1%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 76.4%

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

      7. neg-mul-1 76.4%

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

      8. *-commutative 76.4%

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

      9. associate-*l/ 76.4%

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

      10. clear-num 76.4%

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

      11. associate-*l/ 76.4%

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

      12. metadata-eval 76.4%

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

   7. Applied egg-rr 76.4%

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

   8. Taylor expanded in v around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. associate-/l* 76.4%

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

      3. distribute-rgt-neg-in 76.4%

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

      4. distribute-frac-neg 76.4%

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

      5. neg-sub0 76.4%

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

      6. associate--r- 76.4%

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

      7. metadata-eval 76.4%

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

      8. +-commutative 76.4%

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

   10. Simplified 76.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 5.8 \cdot 10^{-136}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1:\\ \;\;\;\;\frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m + -1}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 10^{-22}:\\ \;\;\;\;\left(m + 1\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(1 + m \cdot \left(m + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1e-22)
   (* (+ m 1.0) (+ -1.0 (/ m v)))
   (* (/ m v) (+ 1.0 (* m (+ m -2.0))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1e-22) {
		tmp = (m + 1.0) * (-1.0 + (m / v));
	} else {
		tmp = (m / v) * (1.0 + (m * (m + -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1d-22) then
        tmp = (m + 1.0d0) * ((-1.0d0) + (m / v))
    else
        tmp = (m / v) * (1.0d0 + (m * (m + (-2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1e-22) {
		tmp = (m + 1.0) * (-1.0 + (m / v));
	} else {
		tmp = (m / v) * (1.0 + (m * (m + -2.0)));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1e-22:
		tmp = (m + 1.0) * (-1.0 + (m / v))
	else:
		tmp = (m / v) * (1.0 + (m * (m + -2.0)))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1e-22)
		tmp = Float64(Float64(m + 1.0) * Float64(-1.0 + Float64(m / v)));
	else
		tmp = Float64(Float64(m / v) * Float64(1.0 + Float64(m * Float64(m + -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1e-22)
		tmp = (m + 1.0) * (-1.0 + (m / v));
	else
		tmp = (m / v) * (1.0 + (m * (m + -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1e-22], N[(N[(m + 1.0), $MachinePrecision] * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m / v), $MachinePrecision] * N[(1.0 + N[(m * N[(m + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in m around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. sub-neg 100.0%

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

      8. metadata-eval 100.0%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 100.0%

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

      11. sqr-neg 100.0%

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

      12. sqrt-unprod 100.0%

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

      13. add-sqr-sqrt 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-rgt1-in 100.0%

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

   7. Simplified 100.0%

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

   if 1e-22 < m

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in m around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. unpow2 99.9%

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

      3. distribute-rgt-out 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 10^{-22}:\\ \;\;\;\;\left(m + 1\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(1 + m \cdot \left(m + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 3.3:\\ \;\;\;\;\left(m + 1\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m \cdot \left(m + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 3.3) (* (+ m 1.0) (+ -1.0 (/ m v))) (* (/ m v) (* m (+ m -2.0)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 3.3) {
		tmp = (m + 1.0) * (-1.0 + (m / v));
	} else {
		tmp = (m / v) * (m * (m + -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 3.3d0) then
        tmp = (m + 1.0d0) * ((-1.0d0) + (m / v))
    else
        tmp = (m / v) * (m * (m + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 3.3) {
		tmp = (m + 1.0) * (-1.0 + (m / v));
	} else {
		tmp = (m / v) * (m * (m + -2.0));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 3.3:
		tmp = (m + 1.0) * (-1.0 + (m / v))
	else:
		tmp = (m / v) * (m * (m + -2.0))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 3.3)
		tmp = Float64(Float64(m + 1.0) * Float64(-1.0 + Float64(m / v)));
	else
		tmp = Float64(Float64(m / v) * Float64(m * Float64(m + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 3.3)
		tmp = (m + 1.0) * (-1.0 + (m / v));
	else
		tmp = (m / v) * (m * (m + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 3.3], N[(N[(m + 1.0), $MachinePrecision] * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m / v), $MachinePrecision] * N[(m * N[(m + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 3.2999999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in m around 0 97.6%

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

      1. sub-neg 97.6%

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

      2. distribute-lft-in 97.6%

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

      3. *-commutative 97.6%

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

      4. *-un-lft-identity 97.6%

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

      5. sub-neg 97.6%

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

      6. metadata-eval 97.6%

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

      7. sub-neg 97.6%

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

      8. metadata-eval 97.6%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 97.4%

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

      11. sqr-neg 97.4%

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

      12. sqrt-unprod 97.4%

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

      13. add-sqr-sqrt 97.4%

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

   5. Applied egg-rr 97.4%

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

      1. *-commutative 97.4%

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

      2. distribute-rgt1-in 97.4%

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

   7. Simplified 97.4%

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

   if 3.2999999999999998 < m

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in m around inf 98.3%

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

      1. +-commutative 98.3%

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

      2. unpow2 98.3%

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

      3. distribute-rgt-out 98.3%

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

   10. Simplified 98.3%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 3.3:\\ \;\;\;\;\left(m + 1\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m \cdot \left(m + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.6:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m \cdot \left(m + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.6) (* (- 1.0 m) (+ -1.0 (/ m v))) (* (/ m v) (* m (+ m -2.0)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.6) {
		tmp = (1.0 - m) * (-1.0 + (m / v));
	} else {
		tmp = (m / v) * (m * (m + -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.6d0) then
        tmp = (1.0d0 - m) * ((-1.0d0) + (m / v))
    else
        tmp = (m / v) * (m * (m + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.6) {
		tmp = (1.0 - m) * (-1.0 + (m / v));
	} else {
		tmp = (m / v) * (m * (m + -2.0));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.6:
		tmp = (1.0 - m) * (-1.0 + (m / v))
	else:
		tmp = (m / v) * (m * (m + -2.0))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.6)
		tmp = Float64(Float64(1.0 - m) * Float64(-1.0 + Float64(m / v)));
	else
		tmp = Float64(Float64(m / v) * Float64(m * Float64(m + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.6)
		tmp = (1.0 - m) * (-1.0 + (m / v));
	else
		tmp = (m / v) * (m * (m + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.6], N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m / v), $MachinePrecision] * N[(m * N[(m + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.6000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in m around 0 97.6%

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

   if 1.6000000000000001 < m

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in m around inf 98.3%

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

      1. +-commutative 98.3%

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

      2. unpow2 98.3%

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

      3. distribute-rgt-out 98.3%

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

   10. Simplified 98.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.6:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v} \cdot \left(m \cdot \left(m + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 100.0%

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

   1. *-commutative 100.0%

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

   2. sub-neg 100.0%

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

   3. associate-/l* 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 10: 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 100.0%

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

   1. *-commutative 100.0%

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

   2. sub-neg 100.0%

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

   3. associate-/l* 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

   1. clear-num 99.8%

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

   2. un-div-inv 99.9%

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

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

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

Alternative 11: 62.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 5.8 \cdot 10^{-136}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= m 5.8e-136) -1.0 (/ m v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 5.8e-136) {
		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 <= 5.8d-136) 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 <= 5.8e-136) {
		tmp = -1.0;
	} else {
		tmp = m / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 5.8e-136:
		tmp = -1.0
	else:
		tmp = m / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 5.8e-136)
		tmp = -1.0;
	else
		tmp = Float64(m / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 5.8e-136)
		tmp = -1.0;
	else
		tmp = m / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 5.8e-136], -1.0, N[(m / v), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 5.79999999999999989e-136

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 71.0%

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

   if 5.79999999999999989e-136 < m

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in v around 0 93.2%

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

   7. Simplified 93.2%

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

   8. Taylor expanded in m around 0 93.2%

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

      1. +-commutative 93.2%

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

      2. unpow2 93.2%

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

      3. distribute-rgt-out 93.2%

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

   10. Simplified 93.2%

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

   11. Taylor expanded in m around 0 58.4%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 5.8 \cdot 10^{-136}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 100.0%

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

   1. *-commutative 100.0%

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

   2. sub-neg 100.0%

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

   3. associate-/l* 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in v around inf 23.9%

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

   1. neg-mul-1 23.9%

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

   2. neg-sub0 23.9%

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

   3. associate--r- 23.9%

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

   4. metadata-eval 23.9%

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

7. Simplified 23.9%

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

8. Final simplification 23.9%

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

Alternative 13: 25.1% 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 100.0%

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

   1. *-commutative 100.0%

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

   2. sub-neg 100.0%

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

   3. associate-/l* 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in m around 0 21.1%

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

6. Final simplification 21.1%

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

Reproduce

herbie shell --seed 2024041 
(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)))