b parameter of renormalized beta distribution

Percentage Accurate: 99.9% → 99.9%

Time: 8.1s

Alternatives: 10

Speedup: N/A×

• 42.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

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, 0.1× speedup

Math

\[\begin{array}{l} \\ \left(-1 + \frac{\frac{{m}^{3} - m}{-1 - m}}{v}\right) \cdot \left(1 - m\right) \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (* (+ -1.0 (/ (/ (- (pow m 3.0) m) (- -1.0 m)) v)) (- 1.0 m)))

C

double code(double m, double v) {
	return (-1.0 + (((pow(m, 3.0) - m) / (-1.0 - m)) / v)) * (1.0 - m);
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    code = ((-1.0d0) + ((((m ** 3.0d0) - m) / ((-1.0d0) - m)) / v)) * (1.0d0 - m)
end function

Java

public static double code(double m, double v) {
	return (-1.0 + (((Math.pow(m, 3.0) - m) / (-1.0 - m)) / v)) * (1.0 - m);
}

Python

def code(m, v):
	return (-1.0 + (((math.pow(m, 3.0) - m) / (-1.0 - m)) / v)) * (1.0 - m)

Julia

function code(m, v)
	return Float64(Float64(-1.0 + Float64(Float64(Float64((m ^ 3.0) - m) / Float64(-1.0 - m)) / v)) * Float64(1.0 - m))
end

MATLAB

function tmp = code(m, v)
	tmp = (-1.0 + ((((m ^ 3.0) - m) / (-1.0 - m)) / v)) * (1.0 - m);
end

Wolfram

code[m_, v_] := N[(N[(-1.0 + N[(N[(N[(N[Power[m, 3.0], $MachinePrecision] - m), $MachinePrecision] / N[(-1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision] * N[(1.0 - m), $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. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 99.9%

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

   2. flip-- 99.9%

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

   3. associate-*l/ 99.9%

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

   4. metadata-eval 99.9%

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

   5. pow2 99.9%

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

   6. +-commutative 99.9%

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

4. Applied egg-rr 99.9%

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

   1. *-commutative 99.9%

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

   2. unpow2 99.9%

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

   3. cancel-sign-sub-inv 99.9%

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

   4. distribute-lft-in 99.9%

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

   5. *-rgt-identity 99.9%

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

   6. distribute-lft-neg-out 99.9%

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

   7. unpow2 99.9%

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

   8. distribute-rgt-neg-in 99.9%

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

   9. unpow2 99.9%

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

   10. cube-mult 99.9%

       \[\leadsto \left(\frac{\frac{m + \left(-\color{blue}{{m}^{3}}\right)}{m + 1}}{v} - 1\right) \cdot \left(1 - m\right) \]

6. Simplified 99.9%

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

   1. frac-2neg 99.9%

      \[\leadsto \left(\frac{\color{blue}{\frac{-\left(m + \left(-{m}^{3}\right)\right)}{-\left(m + 1\right)}}}{v} - 1\right) \cdot \left(1 - m\right) \]

   2. div-inv 99.9%

      \[\leadsto \left(\frac{\color{blue}{\left(-\left(m + \left(-{m}^{3}\right)\right)\right) \cdot \frac{1}{-\left(m + 1\right)}}}{v} - 1\right) \cdot \left(1 - m\right) \]

   3. +-commutative 99.9%

      \[\leadsto \left(\frac{\left(-\color{blue}{\left(\left(-{m}^{3}\right) + m\right)}\right) \cdot \frac{1}{-\left(m + 1\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   4. distribute-neg-in 99.9%

      \[\leadsto \left(\frac{\color{blue}{\left(\left(-\left(-{m}^{3}\right)\right) + \left(-m\right)\right)} \cdot \frac{1}{-\left(m + 1\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   5. add-sqr-sqrt 34.0%

      \[\leadsto \left(\frac{\left(\left(-\color{blue}{\sqrt{-{m}^{3}} \cdot \sqrt{-{m}^{3}}}\right) + \left(-m\right)\right) \cdot \frac{1}{-\left(m + 1\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   6. sqrt-unprod 51.3%

      \[\leadsto \left(\frac{\left(\left(-\color{blue}{\sqrt{\left(-{m}^{3}\right) \cdot \left(-{m}^{3}\right)}}\right) + \left(-m\right)\right) \cdot \frac{1}{-\left(m + 1\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   7. sqr-neg 51.3%

      \[\leadsto \left(\frac{\left(\left(-\sqrt{\color{blue}{{m}^{3} \cdot {m}^{3}}}\right) + \left(-m\right)\right) \cdot \frac{1}{-\left(m + 1\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   8. sqrt-unprod 51.3%

      \[\leadsto \left(\frac{\left(\left(-\color{blue}{\sqrt{{m}^{3}} \cdot \sqrt{{m}^{3}}}\right) + \left(-m\right)\right) \cdot \frac{1}{-\left(m + 1\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   9. add-sqr-sqrt 51.3%

      \[\leadsto \left(\frac{\left(\left(-\color{blue}{{m}^{3}}\right) + \left(-m\right)\right) \cdot \frac{1}{-\left(m + 1\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   10. add-sqr-sqrt 34.0%

       \[\leadsto \left(\frac{\left(\color{blue}{\sqrt{-{m}^{3}} \cdot \sqrt{-{m}^{3}}} + \left(-m\right)\right) \cdot \frac{1}{-\left(m + 1\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   11. sqrt-unprod 99.2%

       \[\leadsto \left(\frac{\left(\color{blue}{\sqrt{\left(-{m}^{3}\right) \cdot \left(-{m}^{3}\right)}} + \left(-m\right)\right) \cdot \frac{1}{-\left(m + 1\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   12. sqr-neg 99.2%

       \[\leadsto \left(\frac{\left(\sqrt{\color{blue}{{m}^{3} \cdot {m}^{3}}} + \left(-m\right)\right) \cdot \frac{1}{-\left(m + 1\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   13. sqrt-unprod 99.9%

       \[\leadsto \left(\frac{\left(\color{blue}{\sqrt{{m}^{3}} \cdot \sqrt{{m}^{3}}} + \left(-m\right)\right) \cdot \frac{1}{-\left(m + 1\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   14. add-sqr-sqrt 99.9%

       \[\leadsto \left(\frac{\left(\color{blue}{{m}^{3}} + \left(-m\right)\right) \cdot \frac{1}{-\left(m + 1\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   15. +-commutative 99.9%

       \[\leadsto \left(\frac{\left({m}^{3} + \left(-m\right)\right) \cdot \frac{1}{-\color{blue}{\left(1 + m\right)}}}{v} - 1\right) \cdot \left(1 - m\right) \]

   16. distribute-neg-in 99.9%

       \[\leadsto \left(\frac{\left({m}^{3} + \left(-m\right)\right) \cdot \frac{1}{\color{blue}{\left(-1\right) + \left(-m\right)}}}{v} - 1\right) \cdot \left(1 - m\right) \]

   17. metadata-eval 99.9%

       \[\leadsto \left(\frac{\left({m}^{3} + \left(-m\right)\right) \cdot \frac{1}{\color{blue}{-1} + \left(-m\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

8. Applied egg-rr 99.9%

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

   1. associate-*r/ 99.9%

      \[\leadsto \left(\frac{\color{blue}{\frac{\left({m}^{3} + \left(-m\right)\right) \cdot 1}{-1 + \left(-m\right)}}}{v} - 1\right) \cdot \left(1 - m\right) \]

   2. *-rgt-identity 99.9%

      \[\leadsto \left(\frac{\frac{\color{blue}{{m}^{3} + \left(-m\right)}}{-1 + \left(-m\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   3. unsub-neg 99.9%

      \[\leadsto \left(\frac{\frac{\color{blue}{{m}^{3} - m}}{-1 + \left(-m\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

   4. unsub-neg 99.9%

      \[\leadsto \left(\frac{\frac{{m}^{3} - m}{\color{blue}{-1 - m}}}{v} - 1\right) \cdot \left(1 - m\right) \]

10. Simplified 99.9%

    \[\leadsto \left(\frac{\color{blue}{\frac{{m}^{3} - m}{-1 - m}}}{v} - 1\right) \cdot \left(1 - m\right) \]

11. Final simplification 99.9%

    \[\leadsto \left(-1 + \frac{\frac{{m}^{3} - m}{-1 - m}}{v}\right) \cdot \left(1 - m\right) \]
12. Add Preprocessing

Alternative 2: 98.1% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in m around 0 97.1%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      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 inf 99.1%

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

      1. neg-mul-1 99.1%

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

      2. distribute-neg-frac2 99.1%

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

   7. Simplified 99.1%

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

4. Final simplification 98.1%

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

Alternative 3: 75.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in m around 0 97.1%

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

   if 1 < m

   1. Initial program 99.9%

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

   3. Taylor expanded in m around 0 0.1%

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

   4. Taylor expanded in v around 0 0.1%

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

   5. Taylor expanded in m around 0 55.7%

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

4. Final simplification 77.4%

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

Alternative 4: 87.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in m around 0 97.1%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      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 inf 99.1%

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

      1. neg-mul-1 99.1%

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

      2. distribute-neg-frac2 99.1%

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

   7. Simplified 99.1%

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

      1. clear-num 99.1%

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

      2. un-div-inv 99.1%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 0.0%

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

      5. sqr-neg 0.0%

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

      6. sqrt-unprod 0.1%

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

      7. add-sqr-sqrt 0.1%

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

   9. Applied egg-rr 0.1%

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

   10. Taylor expanded in m around 0 80.5%

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

4. Final simplification 89.2%

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

Alternative 5: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-/l* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(m / N[(v / N[(1.0 - m), $MachinePrecision]), $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* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

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

Alternative 7: 75.7% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := N[(-1.0 + N[(m * N[(1.0 + N[(1.0 / 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* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in m around 0 77.3%

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

6. Final simplification 77.3%

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

Alternative 8: 62.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.16 \cdot 10^{-139}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= m 1.16e-139) -1.0 (/ m v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.16e-139) {
		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 <= 1.16d-139) 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 <= 1.16e-139) {
		tmp = -1.0;
	} else {
		tmp = m / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.16e-139:
		tmp = -1.0
	else:
		tmp = m / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.16e-139)
		tmp = -1.0;
	else
		tmp = Float64(m / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.16e-139)
		tmp = -1.0;
	else
		tmp = m / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.16e-139], -1.0, N[(m / v), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.15999999999999999e-139

   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 76.4%

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

   if 1.15999999999999999e-139 < 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. Taylor expanded in m around 0 32.4%

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

   4. Taylor expanded in v around 0 24.3%

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

   5. Taylor expanded in m around 0 60.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.16 \cdot 10^{-139}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 27.1% 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* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in v around inf 28.0%

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

   1. neg-mul-1 28.0%

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

   2. sub-neg 28.0%

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

   3. +-commutative 28.0%

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

   4. distribute-neg-in 28.0%

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

   5. remove-double-neg 28.0%

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

   6. metadata-eval 28.0%

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

7. Simplified 28.0%

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

8. Final simplification 28.0%

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

Alternative 10: 24.6% 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* 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in m around 0 25.7%

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

6. Final simplification 25.7%

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

Reproduce

herbie shell --seed 2024078 
(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)))