b parameter of renormalized beta distribution

Percentage Accurate: 99.9% → 99.9%

Time: 8.2s

Alternatives: 10

Speedup: 1.0×

• 42.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 87.1% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in m around 0 99.2%

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

   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%

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

      1. +-commutative 0.1%

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

      2. associate-*r* 0.1%

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

      3. neg-mul-1 0.1%

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

      4. distribute-rgt-out 0.1%

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

      5. unsub-neg 0.1%

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

   6. Simplified 0.1%

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

      1. sub-neg 0.1%

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

      2. distribute-lft-in 0.1%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-prod 74.0%

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

      5. sqr-neg 74.0%

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

      6. pow2 74.0%

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

      7. sqrt-pow1 74.0%

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

      8. metadata-eval 74.0%

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

      9. pow1 74.0%

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

      10. neg-sub0 74.0%

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

      11. associate--r- 74.0%

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

      12. metadata-eval 74.0%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-prod 24.4%

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

      15. sqr-neg 24.4%

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

      16. pow2 24.4%

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

      17. sqrt-pow1 74.0%

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

      18. metadata-eval 74.0%

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

      19. pow1 74.0%

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

      20. neg-sub0 74.0%

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

      21. associate--r- 74.0%

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

      22. metadata-eval 74.0%

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

   8. Applied egg-rr 74.0%

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

      1. distribute-lft-out 74.0%

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

      2. sub-neg 74.0%

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

      3. +-commutative 74.0%

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

   10. Simplified 74.0%

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

   11. Taylor expanded in v around 0 74.0%

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

       1. sub-neg 74.0%

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

       2. metadata-eval 74.0%

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

       3. associate-*l/ 74.0%

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

   13. Simplified 74.0%

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

4. Final simplification 87.1%

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

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

4. Applied egg-rr 99.9%

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

5. Final simplification 99.9%

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

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / m)) + (-1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

   1. associate-*r/ 99.9%

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

   2. *-commutative 99.9%

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

   3. associate-*r/ 99.9%

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

   4. clear-num 99.9%

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

   5. un-div-inv 99.9%

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

6. Applied egg-rr 99.9%

   \[\leadsto \left(1 - m\right) \cdot \left(\color{blue}{\frac{1 - m}{\frac{v}{m}}} + -1\right) \]
7. 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* 99.9%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 6: 87.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1

   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* 99.8%

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

      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 99.0%

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

   6. Taylor expanded in v around 0 99.1%

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

   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%

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

      1. +-commutative 0.1%

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

      2. associate-*r* 0.1%

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

      3. neg-mul-1 0.1%

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

      4. distribute-rgt-out 0.1%

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

      5. unsub-neg 0.1%

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

   6. Simplified 0.1%

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

      1. sub-neg 0.1%

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

      2. distribute-lft-in 0.1%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-prod 74.0%

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

      5. sqr-neg 74.0%

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

      6. pow2 74.0%

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

      7. sqrt-pow1 74.0%

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

      8. metadata-eval 74.0%

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

      9. pow1 74.0%

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

      10. neg-sub0 74.0%

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

      11. associate--r- 74.0%

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

      12. metadata-eval 74.0%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-prod 24.4%

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

      15. sqr-neg 24.4%

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

      16. pow2 24.4%

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

      17. sqrt-pow1 74.0%

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

      18. metadata-eval 74.0%

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

      19. pow1 74.0%

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

      20. neg-sub0 74.0%

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

      21. associate--r- 74.0%

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

      22. metadata-eval 74.0%

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

   8. Applied egg-rr 74.0%

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

      1. distribute-lft-out 74.0%

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

      2. sub-neg 74.0%

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

      3. +-commutative 74.0%

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

   10. Simplified 74.0%

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

   11. Taylor expanded in v around 0 74.0%

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

       1. sub-neg 74.0%

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

       2. metadata-eval 74.0%

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

       3. associate-*l/ 74.0%

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

   13. Simplified 74.0%

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

4. Final simplification 87.0%

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

Alternative 7: 62.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 9 \cdot 10^{-119}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= m 9e-119) -1.0 (/ m v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 9e-119) {
		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 <= 9d-119) 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 <= 9e-119) {
		tmp = -1.0;
	} else {
		tmp = m / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 9e-119:
		tmp = -1.0
	else:
		tmp = m / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 9e-119)
		tmp = -1.0;
	else
		tmp = Float64(m / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 9e-119)
		tmp = -1.0;
	else
		tmp = m / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 9e-119], -1.0, N[(m / v), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 9.0000000000000005e-119

   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%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in m around 0 73.7%

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

   if 9.0000000000000005e-119 < 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 27.1%

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

   4. Taylor expanded in v around 0 27.1%

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

      1. +-commutative 27.1%

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

      2. associate-*r* 27.1%

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

      3. neg-mul-1 27.1%

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

      4. distribute-rgt-out 27.1%

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

      5. unsub-neg 27.1%

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

   6. Simplified 27.1%

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

   7. Taylor expanded in v around 0 21.9%

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

      1. associate-/l* 21.8%

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

   9. Simplified 21.8%

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

   10. Taylor expanded in m around 0 60.6%

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

Alternative 8: 75.4% accurate, 2.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   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 77.2%

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

6. Taylor expanded in v around 0 77.3%

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

7. Final simplification 77.3%

   \[\leadsto \frac{m}{v} + -1 \]
8. Add Preprocessing

Alternative 9: 26.7% 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%

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

   4. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in v around inf 30.8%

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

   1. neg-mul-1 30.8%

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

   2. neg-sub0 30.8%

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

   3. associate--r- 30.8%

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

   4. metadata-eval 30.8%

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

7. Simplified 30.8%

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

8. Final simplification 30.8%

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

Alternative 10: 24.3% 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%

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

   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 28.5%

   \[\leadsto \color{blue}{-1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024092 
(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)))