b parameter of renormalized beta distribution

Percentage Accurate: 99.9% → 99.9%

Time: 6.3s

Alternatives: 12

Speedup: N/A×

• 40.8% 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

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

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* 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. Final simplification 99.9%

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

Alternative 2: 80.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := m + \frac{m}{v}\\ \mathbf{if}\;m \leq 6 \cdot 10^{-248}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1.55 \cdot 10^{-220}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;m \leq 1.08 \cdot 10^{-201}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 0.38:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(m \cdot \frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (let* ((t_0 (+ m (/ m v))))
   (if (<= m 6e-248)
     -1.0
     (if (<= m 1.55e-220)
       t_0
       (if (<= m 1.08e-201) -1.0 (if (<= m 0.38) t_0 (* m (* m (/ m v)))))))))

C

double code(double m, double v) {
	double t_0 = m + (m / v);
	double tmp;
	if (m <= 6e-248) {
		tmp = -1.0;
	} else if (m <= 1.55e-220) {
		tmp = t_0;
	} else if (m <= 1.08e-201) {
		tmp = -1.0;
	} else if (m <= 0.38) {
		tmp = t_0;
	} else {
		tmp = m * (m * (m / v));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: t_0
    real(8) :: tmp
    t_0 = m + (m / v)
    if (m <= 6d-248) then
        tmp = -1.0d0
    else if (m <= 1.55d-220) then
        tmp = t_0
    else if (m <= 1.08d-201) then
        tmp = -1.0d0
    else if (m <= 0.38d0) then
        tmp = t_0
    else
        tmp = m * (m * (m / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double t_0 = m + (m / v);
	double tmp;
	if (m <= 6e-248) {
		tmp = -1.0;
	} else if (m <= 1.55e-220) {
		tmp = t_0;
	} else if (m <= 1.08e-201) {
		tmp = -1.0;
	} else if (m <= 0.38) {
		tmp = t_0;
	} else {
		tmp = m * (m * (m / v));
	}
	return tmp;
}

Python

def code(m, v):
	t_0 = m + (m / v)
	tmp = 0
	if m <= 6e-248:
		tmp = -1.0
	elif m <= 1.55e-220:
		tmp = t_0
	elif m <= 1.08e-201:
		tmp = -1.0
	elif m <= 0.38:
		tmp = t_0
	else:
		tmp = m * (m * (m / v))
	return tmp

Julia

function code(m, v)
	t_0 = Float64(m + Float64(m / v))
	tmp = 0.0
	if (m <= 6e-248)
		tmp = -1.0;
	elseif (m <= 1.55e-220)
		tmp = t_0;
	elseif (m <= 1.08e-201)
		tmp = -1.0;
	elseif (m <= 0.38)
		tmp = t_0;
	else
		tmp = Float64(m * Float64(m * Float64(m / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	t_0 = m + (m / v);
	tmp = 0.0;
	if (m <= 6e-248)
		tmp = -1.0;
	elseif (m <= 1.55e-220)
		tmp = t_0;
	elseif (m <= 1.08e-201)
		tmp = -1.0;
	elseif (m <= 0.38)
		tmp = t_0;
	else
		tmp = m * (m * (m / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := Block[{t$95$0 = N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[m, 6e-248], -1.0, If[LessEqual[m, 1.55e-220], t$95$0, If[LessEqual[m, 1.08e-201], -1.0, If[LessEqual[m, 0.38], t$95$0, N[(m * N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if m < 6.00000000000000027e-248 or 1.55000000000000006e-220 < m < 1.0799999999999999e-201

   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%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 93.0%

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

   if 6.00000000000000027e-248 < m < 1.55000000000000006e-220 or 1.0799999999999999e-201 < m < 0.38

   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 92.8%

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

   3. Taylor expanded in m around inf 75.5%

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

      1. +-commutative 75.5%

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

      2. mul-1-neg 75.5%

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

      3. unpow2 75.5%

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

      4. associate-*r/ 75.5%

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

      5. unsub-neg 75.5%

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

      6. *-commutative 75.5%

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

      7. distribute-lft-in 75.5%

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

      8. *-rgt-identity 75.5%

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

      9. associate-*r/ 75.8%

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

      10. *-rgt-identity 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in m around 0 75.3%

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

      1. *-commutative 75.3%

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

      2. distribute-lft-in 75.3%

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

      3. *-rgt-identity 75.3%

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

      4. associate-*r/ 75.5%

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

      5. *-rgt-identity 75.5%

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

   8. Simplified 75.5%

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

   if 0.38 < 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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around inf 97.6%

      \[\leadsto \color{blue}{\frac{{m}^{3}}{v}} \]
   5. Step-by-step derivation

      1. div-inv 97.6%

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

      2. cube-mult 97.6%

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

      3. associate-*l* 97.6%

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

      4. add-sqr-sqrt 97.6%

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

      5. sqrt-unprod 97.6%

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

      6. sqr-neg 97.6%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 0.1%

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

      9. associate-*l* 0.1%

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

      10. div-inv 0.1%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 97.6%

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

      13. sqr-neg 97.6%

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

      14. sqrt-unprod 97.6%

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

      15. add-sqr-sqrt 97.6%

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

   6. Applied egg-rr 97.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 6 \cdot 10^{-248}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1.55 \cdot 10^{-220}:\\ \;\;\;\;m + \frac{m}{v}\\ \mathbf{elif}\;m \leq 1.08 \cdot 10^{-201}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 0.38:\\ \;\;\;\;m + \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(m \cdot \frac{m}{v}\right)\\ \end{array} \]

Alternative 3: 80.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := m + \frac{m}{v}\\ \mathbf{if}\;m \leq 6 \cdot 10^{-248}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1.45 \cdot 10^{-220}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;m \leq 6.8 \cdot 10^{-202}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 0.38:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m \cdot m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (let* ((t_0 (+ m (/ m v))))
   (if (<= m 6e-248)
     -1.0
     (if (<= m 1.45e-220)
       t_0
       (if (<= m 6.8e-202) -1.0 (if (<= m 0.38) t_0 (* m (/ (* m m) v))))))))

C

double code(double m, double v) {
	double t_0 = m + (m / v);
	double tmp;
	if (m <= 6e-248) {
		tmp = -1.0;
	} else if (m <= 1.45e-220) {
		tmp = t_0;
	} else if (m <= 6.8e-202) {
		tmp = -1.0;
	} else if (m <= 0.38) {
		tmp = t_0;
	} else {
		tmp = m * ((m * m) / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: t_0
    real(8) :: tmp
    t_0 = m + (m / v)
    if (m <= 6d-248) then
        tmp = -1.0d0
    else if (m <= 1.45d-220) then
        tmp = t_0
    else if (m <= 6.8d-202) then
        tmp = -1.0d0
    else if (m <= 0.38d0) then
        tmp = t_0
    else
        tmp = m * ((m * m) / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double t_0 = m + (m / v);
	double tmp;
	if (m <= 6e-248) {
		tmp = -1.0;
	} else if (m <= 1.45e-220) {
		tmp = t_0;
	} else if (m <= 6.8e-202) {
		tmp = -1.0;
	} else if (m <= 0.38) {
		tmp = t_0;
	} else {
		tmp = m * ((m * m) / v);
	}
	return tmp;
}

Python

def code(m, v):
	t_0 = m + (m / v)
	tmp = 0
	if m <= 6e-248:
		tmp = -1.0
	elif m <= 1.45e-220:
		tmp = t_0
	elif m <= 6.8e-202:
		tmp = -1.0
	elif m <= 0.38:
		tmp = t_0
	else:
		tmp = m * ((m * m) / v)
	return tmp

Julia

function code(m, v)
	t_0 = Float64(m + Float64(m / v))
	tmp = 0.0
	if (m <= 6e-248)
		tmp = -1.0;
	elseif (m <= 1.45e-220)
		tmp = t_0;
	elseif (m <= 6.8e-202)
		tmp = -1.0;
	elseif (m <= 0.38)
		tmp = t_0;
	else
		tmp = Float64(m * Float64(Float64(m * m) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	t_0 = m + (m / v);
	tmp = 0.0;
	if (m <= 6e-248)
		tmp = -1.0;
	elseif (m <= 1.45e-220)
		tmp = t_0;
	elseif (m <= 6.8e-202)
		tmp = -1.0;
	elseif (m <= 0.38)
		tmp = t_0;
	else
		tmp = m * ((m * m) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := Block[{t$95$0 = N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[m, 6e-248], -1.0, If[LessEqual[m, 1.45e-220], t$95$0, If[LessEqual[m, 6.8e-202], -1.0, If[LessEqual[m, 0.38], t$95$0, N[(m * N[(N[(m * m), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if m < 6.00000000000000027e-248 or 1.4499999999999999e-220 < m < 6.80000000000000025e-202

   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%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 93.0%

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

   if 6.00000000000000027e-248 < m < 1.4499999999999999e-220 or 6.80000000000000025e-202 < m < 0.38

   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 92.8%

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

   3. Taylor expanded in m around inf 75.5%

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

      1. +-commutative 75.5%

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

      2. mul-1-neg 75.5%

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

      3. unpow2 75.5%

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

      4. associate-*r/ 75.5%

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

      5. unsub-neg 75.5%

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

      6. *-commutative 75.5%

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

      7. distribute-lft-in 75.5%

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

      8. *-rgt-identity 75.5%

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

      9. associate-*r/ 75.8%

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

      10. *-rgt-identity 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in m around 0 75.3%

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

      1. *-commutative 75.3%

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

      2. distribute-lft-in 75.3%

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

      3. *-rgt-identity 75.3%

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

      4. associate-*r/ 75.5%

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

      5. *-rgt-identity 75.5%

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

   8. Simplified 75.5%

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

   if 0.38 < 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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around inf 97.6%

      \[\leadsto \color{blue}{\frac{{m}^{3}}{v}} \]
   5. Step-by-step derivation

      1. div-inv 97.6%

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

      2. cube-mult 97.6%

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

      3. associate-*l* 97.6%

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

      4. add-sqr-sqrt 97.6%

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

      5. sqrt-unprod 97.6%

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

      6. sqr-neg 97.6%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 0.1%

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

      9. associate-*l* 0.1%

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

      10. div-inv 0.1%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 97.6%

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

      13. sqr-neg 97.6%

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

      14. sqrt-unprod 97.6%

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

      15. add-sqr-sqrt 97.6%

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

   6. Applied egg-rr 97.6%

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

      1. associate-*r/ 97.7%

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

   8. Applied egg-rr 97.7%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 6 \cdot 10^{-248}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1.45 \cdot 10^{-220}:\\ \;\;\;\;m + \frac{m}{v}\\ \mathbf{elif}\;m \leq 6.8 \cdot 10^{-202}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 0.38:\\ \;\;\;\;m + \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m \cdot m}{v}\\ \end{array} \]

Alternative 4: 80.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 6 \cdot 10^{-248}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 2.4 \cdot 10^{-220}:\\ \;\;\;\;m + \frac{m}{v}\\ \mathbf{elif}\;m \leq 1.15 \cdot 10^{-201}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 0.42:\\ \;\;\;\;\left(1 - m\right) \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m \cdot m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 6e-248)
   -1.0
   (if (<= m 2.4e-220)
     (+ m (/ m v))
     (if (<= m 1.15e-201)
       -1.0
       (if (<= m 0.42) (* (- 1.0 m) (/ m v)) (* m (/ (* m m) v)))))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 6e-248) {
		tmp = -1.0;
	} else if (m <= 2.4e-220) {
		tmp = m + (m / v);
	} else if (m <= 1.15e-201) {
		tmp = -1.0;
	} else if (m <= 0.42) {
		tmp = (1.0 - m) * (m / v);
	} else {
		tmp = m * ((m * m) / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 6d-248) then
        tmp = -1.0d0
    else if (m <= 2.4d-220) then
        tmp = m + (m / v)
    else if (m <= 1.15d-201) then
        tmp = -1.0d0
    else if (m <= 0.42d0) then
        tmp = (1.0d0 - m) * (m / v)
    else
        tmp = m * ((m * m) / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 6e-248) {
		tmp = -1.0;
	} else if (m <= 2.4e-220) {
		tmp = m + (m / v);
	} else if (m <= 1.15e-201) {
		tmp = -1.0;
	} else if (m <= 0.42) {
		tmp = (1.0 - m) * (m / v);
	} else {
		tmp = m * ((m * m) / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 6e-248:
		tmp = -1.0
	elif m <= 2.4e-220:
		tmp = m + (m / v)
	elif m <= 1.15e-201:
		tmp = -1.0
	elif m <= 0.42:
		tmp = (1.0 - m) * (m / v)
	else:
		tmp = m * ((m * m) / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 6e-248)
		tmp = -1.0;
	elseif (m <= 2.4e-220)
		tmp = Float64(m + Float64(m / v));
	elseif (m <= 1.15e-201)
		tmp = -1.0;
	elseif (m <= 0.42)
		tmp = Float64(Float64(1.0 - m) * Float64(m / v));
	else
		tmp = Float64(m * Float64(Float64(m * m) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 6e-248)
		tmp = -1.0;
	elseif (m <= 2.4e-220)
		tmp = m + (m / v);
	elseif (m <= 1.15e-201)
		tmp = -1.0;
	elseif (m <= 0.42)
		tmp = (1.0 - m) * (m / v);
	else
		tmp = m * ((m * m) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 6e-248], -1.0, If[LessEqual[m, 2.4e-220], N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 1.15e-201], -1.0, If[LessEqual[m, 0.42], N[(N[(1.0 - m), $MachinePrecision] * N[(m / v), $MachinePrecision]), $MachinePrecision], N[(m * N[(N[(m * m), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if m < 6.00000000000000027e-248 or 2.4000000000000001e-220 < m < 1.14999999999999993e-201

   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%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 93.0%

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

   if 6.00000000000000027e-248 < m < 2.4000000000000001e-220

   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%

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

   3. Taylor expanded in m around inf 83.9%

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

      1. +-commutative 83.9%

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

      2. mul-1-neg 83.9%

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

      3. unpow2 83.9%

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

      4. associate-*r/ 83.9%

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

      5. unsub-neg 83.9%

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

      6. *-commutative 83.9%

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

      7. distribute-lft-in 83.9%

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

      8. *-rgt-identity 83.9%

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

      9. associate-*r/ 84.4%

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

      10. *-rgt-identity 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in m around 0 83.9%

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

      1. *-commutative 83.9%

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

      2. distribute-lft-in 83.9%

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

      3. *-rgt-identity 83.9%

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

      4. associate-*r/ 84.4%

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

      5. *-rgt-identity 84.4%

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

   8. Simplified 84.4%

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

   if 1.14999999999999993e-201 < m < 0.419999999999999984

   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 92.1%

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

   3. Taylor expanded in m around inf 74.7%

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

      1. +-commutative 74.7%

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

      2. mul-1-neg 74.7%

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

      3. unpow2 74.7%

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

      4. associate-*r/ 74.7%

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

      5. unsub-neg 74.7%

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

      6. *-commutative 74.7%

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

      7. distribute-lft-in 74.7%

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

      8. *-rgt-identity 74.7%

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

      9. associate-*r/ 74.9%

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

      10. *-rgt-identity 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in v around 0 74.9%

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

      1. unpow2 74.9%

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

      2. div-sub 74.9%

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

      3. associate-*r/ 74.9%

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

      4. cancel-sign-sub-inv 74.9%

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

      5. *-lft-identity 74.9%

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

      6. distribute-rgt-in 74.9%

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

      7. sub-neg 74.9%

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

   8. Simplified 74.9%

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

   if 0.419999999999999984 < 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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around inf 97.6%

      \[\leadsto \color{blue}{\frac{{m}^{3}}{v}} \]
   5. Step-by-step derivation

      1. div-inv 97.6%

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

      2. cube-mult 97.6%

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

      3. associate-*l* 97.6%

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

      4. add-sqr-sqrt 97.6%

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

      5. sqrt-unprod 97.6%

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

      6. sqr-neg 97.6%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 0.1%

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

      9. associate-*l* 0.1%

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

      10. div-inv 0.1%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 97.6%

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

      13. sqr-neg 97.6%

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

      14. sqrt-unprod 97.6%

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

      15. add-sqr-sqrt 97.6%

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

   6. Applied egg-rr 97.6%

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

      1. associate-*r/ 97.7%

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

   8. Applied egg-rr 97.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 6 \cdot 10^{-248}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 2.4 \cdot 10^{-220}:\\ \;\;\;\;m + \frac{m}{v}\\ \mathbf{elif}\;m \leq 1.15 \cdot 10^{-201}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 0.42:\\ \;\;\;\;\left(1 - m\right) \cdot \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m \cdot m}{v}\\ \end{array} \]

Alternative 5: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := If[LessEqual[m, 1.65], N[(N[(m / N[(v / N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(m + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision] * N[(m + -2.0), $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 93.9%

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

   3. Taylor expanded in v around 0 93.9%

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

      1. +-commutative 93.9%

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

      2. mul-1-neg 93.9%

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

      3. unsub-neg 93.9%

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

      4. associate-/l* 93.9%

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

   5. Simplified 93.9%

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

   if 1.6499999999999999 < m

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. div-inv 99.9%

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

      3. associate-/r* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in m around inf 18.5%

      \[\leadsto \color{blue}{-2 \cdot \frac{{m}^{2}}{v} + \frac{{m}^{3}}{v}} \]
   7. Step-by-step derivation

      1. unpow2 18.5%

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

      2. associate-*r/ 18.5%

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

      3. unpow3 18.5%

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

      4. associate-*r/ 18.5%

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

      5. associate-*r* 18.5%

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

      6. distribute-rgt-out 98.6%

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

   8. Simplified 98.6%

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

4. Final simplification 96.5%

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

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(N[(1.0 - m), $MachinePrecision] * N[(m / 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/ 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 7: 58.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 6 \cdot 10^{-248}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1.45 \cdot 10^{-220} \lor \neg \left(m \leq 1.6 \cdot 10^{-201}\right):\\ \;\;\;\;m + \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 6e-248)
   -1.0
   (if (or (<= m 1.45e-220) (not (<= m 1.6e-201))) (+ m (/ m v)) -1.0)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 6e-248) {
		tmp = -1.0;
	} else if ((m <= 1.45e-220) || !(m <= 1.6e-201)) {
		tmp = m + (m / v);
	} else {
		tmp = -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-248) then
        tmp = -1.0d0
    else if ((m <= 1.45d-220) .or. (.not. (m <= 1.6d-201))) then
        tmp = m + (m / v)
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 6e-248) {
		tmp = -1.0;
	} else if ((m <= 1.45e-220) || !(m <= 1.6e-201)) {
		tmp = m + (m / v);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 6e-248:
		tmp = -1.0
	elif (m <= 1.45e-220) or not (m <= 1.6e-201):
		tmp = m + (m / v)
	else:
		tmp = -1.0
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 6e-248)
		tmp = -1.0;
	elseif ((m <= 1.45e-220) || !(m <= 1.6e-201))
		tmp = Float64(m + Float64(m / v));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 6e-248)
		tmp = -1.0;
	elseif ((m <= 1.45e-220) || ~((m <= 1.6e-201)))
		tmp = m + (m / v);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 6e-248], -1.0, If[Or[LessEqual[m, 1.45e-220], N[Not[LessEqual[m, 1.6e-201]], $MachinePrecision]], N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if m < 6.00000000000000027e-248 or 1.4499999999999999e-220 < m < 1.6000000000000001e-201

   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%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 93.0%

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

   if 6.00000000000000027e-248 < m < 1.4499999999999999e-220 or 1.6000000000000001e-201 < 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 35.1%

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

   3. Taylor expanded in m around inf 28.6%

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

      1. +-commutative 28.6%

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

      2. mul-1-neg 28.6%

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

      3. unpow2 28.6%

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

      4. associate-*r/ 28.6%

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

      5. unsub-neg 28.6%

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

      6. *-commutative 28.6%

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

      7. distribute-lft-in 28.6%

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

      8. *-rgt-identity 28.6%

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

      9. associate-*r/ 28.7%

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

      10. *-rgt-identity 28.7%

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

   5. Simplified 28.7%

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

   6. Taylor expanded in m around 0 62.8%

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

      1. *-commutative 62.8%

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

      2. distribute-lft-in 62.8%

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

      3. *-rgt-identity 62.8%

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

      4. associate-*r/ 62.9%

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

      5. *-rgt-identity 62.9%

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

   8. Simplified 62.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 6 \cdot 10^{-248}:\\ \;\;\;\;-1\\ \mathbf{elif}\;m \leq 1.45 \cdot 10^{-220} \lor \neg \left(m \leq 1.6 \cdot 10^{-201}\right):\\ \;\;\;\;m + \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8: 98.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.4:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(m \cdot \frac{m}{v}\right) \cdot \left(m + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 2.4) (+ -1.0 (+ m (/ m v))) (* (* m (/ m v)) (+ m -2.0))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.4) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m * (m / v)) * (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 <= 2.4d0) then
        tmp = (-1.0d0) + (m + (m / v))
    else
        tmp = (m * (m / v)) * (m + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 2.4) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m * (m / v)) * (m + -2.0);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.4:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = (m * (m / v)) * (m + -2.0)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.4)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(Float64(m * Float64(m / v)) * Float64(m + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.4)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = (m * (m / v)) * (m + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.4], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision] * N[(m + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.39999999999999991

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around 0 93.5%

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

      1. sub-neg 93.5%

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

      2. *-commutative 93.5%

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

      3. distribute-rgt-in 93.5%

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

      4. *-lft-identity 93.5%

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

      5. associate-*l/ 93.7%

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

      6. *-lft-identity 93.7%

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

      7. metadata-eval 93.7%

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

   6. Simplified 93.7%

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

   if 2.39999999999999991 < m

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. div-inv 99.9%

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

      3. associate-/r* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in m around inf 18.5%

      \[\leadsto \color{blue}{-2 \cdot \frac{{m}^{2}}{v} + \frac{{m}^{3}}{v}} \]
   7. Step-by-step derivation

      1. unpow2 18.5%

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

      2. associate-*r/ 18.5%

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

      3. unpow3 18.5%

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

      4. associate-*r/ 18.5%

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

      5. associate-*r* 18.5%

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

      6. distribute-rgt-out 98.6%

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

   8. Simplified 98.6%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.4:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(m \cdot \frac{m}{v}\right) \cdot \left(m + -2\right)\\ \end{array} \]

Alternative 9: 98.3% accurate, 1.2× speedup

Math

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

FPCore

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

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 / v)) * (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 <= 1.65d0) then
        tmp = (1.0d0 - m) * ((-1.0d0) + (m / v))
    else
        tmp = (m * (m / v)) * (m + (-2.0d0))
    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 / v)) * (m + -2.0);
	}
	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 / v)) * (m + -2.0)
	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 / v)) * Float64(m + -2.0));
	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 / v)) * (m + -2.0);
	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 / v), $MachinePrecision]), $MachinePrecision] * N[(m + -2.0), $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 93.9%

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

   if 1.6499999999999999 < m

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. div-inv 99.9%

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

      3. associate-/r* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in m around inf 18.5%

      \[\leadsto \color{blue}{-2 \cdot \frac{{m}^{2}}{v} + \frac{{m}^{3}}{v}} \]
   7. Step-by-step derivation

      1. unpow2 18.5%

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

      2. associate-*r/ 18.5%

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

      3. unpow3 18.5%

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

      4. associate-*r/ 18.5%

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

      5. associate-*r* 18.5%

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

      6. distribute-rgt-out 98.6%

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

   8. Simplified 98.6%

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

4. Final simplification 96.5%

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

Alternative 10: 97.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 0.38:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m \cdot m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 0.38) (+ -1.0 (+ m (/ m v))) (* m (/ (* m m) v))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 0.38) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = m * ((m * m) / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 0.38d0) then
        tmp = (-1.0d0) + (m + (m / v))
    else
        tmp = m * ((m * m) / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 0.38) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = m * ((m * m) / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 0.38:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = m * ((m * m) / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 0.38)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(m * Float64(Float64(m * m) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 0.38)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = m * ((m * m) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 0.38], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(m * N[(N[(m * m), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 0.38

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around 0 94.2%

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

      1. sub-neg 94.2%

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

      2. *-commutative 94.2%

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

      3. distribute-rgt-in 94.2%

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

      4. *-lft-identity 94.2%

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

      5. associate-*l/ 94.4%

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

      6. *-lft-identity 94.4%

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

      7. metadata-eval 94.4%

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

   6. Simplified 94.4%

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

   if 0.38 < 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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around inf 97.6%

      \[\leadsto \color{blue}{\frac{{m}^{3}}{v}} \]
   5. Step-by-step derivation

      1. div-inv 97.6%

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

      2. cube-mult 97.6%

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

      3. associate-*l* 97.6%

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

      4. add-sqr-sqrt 97.6%

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

      5. sqrt-unprod 97.6%

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

      6. sqr-neg 97.6%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 0.1%

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

      9. associate-*l* 0.1%

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

      10. div-inv 0.1%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 97.6%

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

      13. sqr-neg 97.6%

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

      14. sqrt-unprod 97.6%

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

      15. add-sqr-sqrt 97.6%

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

   6. Applied egg-rr 97.6%

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

      1. associate-*r/ 97.7%

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

   8. Applied egg-rr 97.7%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 0.38:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m \cdot m}{v}\\ \end{array} \]

Alternative 11: 27.4% 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/ 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in v around inf 18.6%

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

   1. neg-mul-1 18.6%

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

   2. neg-sub0 18.6%

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

   3. associate--r- 18.6%

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

   4. metadata-eval 18.6%

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

6. Simplified 18.6%

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

7. Final simplification 18.6%

   \[\leadsto m + -1 \]

Alternative 12: 25.0% 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/ 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in m around 0 15.8%

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

5. Final simplification 15.8%

   \[\leadsto -1 \]

Reproduce

herbie shell --seed 2023189 
(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)))