b parameter of renormalized beta distribution

Percentage Accurate: 99.9% → 99.9%

Time: 8.6s

Alternatives: 15

Speedup: 1.0×

• 42.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := N[(N[(m + -1.0), $MachinePrecision] * N[(N[(v + N[(m * N[(m + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / v), $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 v around 0 99.9%

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

   1. neg-mul-1 99.9%

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

   2. +-commutative 99.9%

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

   3. unsub-neg 99.9%

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

7. Simplified 99.9%

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

8. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.25 \cdot 10^{-18}:\\ \;\;\;\;-1 + \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;\left(m + -1\right) \cdot \left(m \cdot \frac{m + -1}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.25e-18) (+ -1.0 (/ m v)) (* (+ m -1.0) (* m (/ (+ m -1.0) v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.25e-18) {
		tmp = -1.0 + (m / v);
	} else {
		tmp = (m + -1.0) * (m * ((m + -1.0) / v));
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.25d-18) then
        tmp = (-1.0d0) + (m / v)
    else
        tmp = (m + (-1.0d0)) * (m * ((m + (-1.0d0)) / v))
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.25e-18) {
		tmp = -1.0 + (m / v);
	} else {
		tmp = (m + -1.0) * (m * ((m + -1.0) / v));
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.25e-18:
		tmp = -1.0 + (m / v)
	else:
		tmp = (m + -1.0) * (m * ((m + -1.0) / v))
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.25e-18)
		tmp = Float64(-1.0 + Float64(m / v));
	else
		tmp = Float64(Float64(m + -1.0) * Float64(m * Float64(Float64(m + -1.0) / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.25e-18)
		tmp = -1.0 + (m / v);
	else
		tmp = (m + -1.0) * (m * ((m + -1.0) / v));
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.25e-18], N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision], N[(N[(m + -1.0), $MachinePrecision] * N[(m * N[(N[(m + -1.0), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.25000000000000009e-18

   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 99.8%

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

      1. +-commutative 40.5%

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

      2. distribute-lft-in 40.5%

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

      3. div-inv 40.7%

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

      4. *-rgt-identity 40.7%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in v around 0 100.0%

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

   if 1.25000000000000009e-18 < 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 v around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. associate-*r/ 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.25 \cdot 10^{-18}:\\ \;\;\;\;-1 + \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;\left(m + -1\right) \cdot \left(m \cdot \frac{m + -1}{v}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.25 \cdot 10^{-18}:\\ \;\;\;\;-1 + \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(\left(1 - m\right) \cdot \frac{m}{v}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.25e-18) (+ -1.0 (/ m v)) (* (- 1.0 m) (* (- 1.0 m) (/ m v)))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.25e-18) {
		tmp = -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 <= 1.25d-18) then
        tmp = (-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 <= 1.25e-18) {
		tmp = -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 <= 1.25e-18:
		tmp = -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 <= 1.25e-18)
		tmp = Float64(-1.0 + Float64(m / v));
	else
		tmp = Float64(Float64(1.0 - m) * Float64(Float64(1.0 - m) * Float64(m / v)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.25e-18)
		tmp = -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, 1.25e-18], N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - m), $MachinePrecision] * N[(N[(1.0 - m), $MachinePrecision] * N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.25000000000000009e-18

   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 99.8%

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

      1. +-commutative 40.5%

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

      2. distribute-lft-in 40.5%

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

      3. div-inv 40.7%

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

      4. *-rgt-identity 40.7%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in v around 0 100.0%

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

   if 1.25000000000000009e-18 < 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 v around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. associate-*r/ 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in m around 0 99.9%

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

       1. +-commutative 99.9%

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

       2. neg-mul-1 99.9%

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

       3. sub-neg 99.9%

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

       4. div-sub 99.9%

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

       5. associate-*r/ 99.9%

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

       6. associate-*l/ 99.9%

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

   13. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.25 \cdot 10^{-18}:\\ \;\;\;\;-1 + \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(\left(1 - m\right) \cdot \frac{m}{v}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.4% accurate, 0.9× speedup

Math

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

FPCore

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

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) * (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) * ((-1.0d0) + (m / v))
    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) * (-1.0 + (m / v));
	} else {
		tmp = (m / v) * (m + -1.0);
	}
	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) * (m + -1.0)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.0)
		tmp = Float64(Float64(1.0 - m) * Float64(-1.0 + Float64(m / v)));
	else
		tmp = Float64(Float64(m / 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) * (-1.0 + (m / v));
	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[(-1.0 + N[(m / v), $MachinePrecision]), $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 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* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in m around 0 97.0%

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

   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 v around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. associate-*r/ 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in m around 0 0.1%

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

       1. associate-*r* 0.1%

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

       2. *-commutative 0.1%

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

       3. div-inv 0.1%

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

       4. frac-2neg 0.1%

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

       5. distribute-rgt-neg-in 0.1%

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

       6. add-sqr-sqrt 0.0%

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

       7. sqrt-unprod 84.2%

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

       8. sqr-neg 84.2%

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

       9. sqrt-unprod 84.2%

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

       10. add-sqr-sqrt 84.2%

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

   13. Applied egg-rr 84.2%

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

       1. associate-/l* 84.2%

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

       2. neg-sub0 84.2%

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

       3. associate--r- 84.2%

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

       4. metadata-eval 84.2%

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

       5. +-commutative 84.2%

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

       6. associate-*r/ 84.2%

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

       7. associate-*l/ 84.2%

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

   15. Simplified 84.2%

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

4. Final simplification 90.4%

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

Alternative 5: 87.4% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.0)
		tmp = Float64(Float64(Float64(1.0 - m) * Float64(m - v)) / v);
	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)) / v;
	else
		tmp = (m / v) * (m + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.0], N[(N[(N[(1.0 - m), $MachinePrecision] * N[(m - v), $MachinePrecision]), $MachinePrecision] / v), $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 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* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in m around 0 97.0%

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

   6. Taylor expanded in v around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. associate-*r* 97.0%

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

      3. neg-mul-1 97.0%

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

      4. distribute-rgt-out 97.0%

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

      5. unsub-neg 97.0%

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

   8. Simplified 97.0%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. associate-*r/ 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in m around 0 0.1%

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

       1. associate-*r* 0.1%

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

       2. *-commutative 0.1%

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

       3. div-inv 0.1%

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

       4. frac-2neg 0.1%

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

       5. distribute-rgt-neg-in 0.1%

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

       6. add-sqr-sqrt 0.0%

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

       7. sqrt-unprod 84.2%

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

       8. sqr-neg 84.2%

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

       9. sqrt-unprod 84.2%

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

       10. add-sqr-sqrt 84.2%

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

   13. Applied egg-rr 84.2%

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

       1. associate-/l* 84.2%

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

       2. neg-sub0 84.2%

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

       3. associate--r- 84.2%

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

       4. metadata-eval 84.2%

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

       5. +-commutative 84.2%

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

       6. associate-*r/ 84.2%

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

       7. associate-*l/ 84.2%

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

   15. Simplified 84.2%

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

4. Final simplification 90.4%

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

Alternative 6: 97.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.0)
		tmp = Float64(Float64(Float64(1.0 - m) * Float64(m - v)) / v);
	else
		tmp = Float64(Float64(m * 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)) / v;
	else
		tmp = (m * (m / v)) * (m + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.0], N[(N[(N[(1.0 - m), $MachinePrecision] * N[(m - v), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision], N[(N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision] * N[(m + -1.0), $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. 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* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in m around 0 97.0%

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

   6. Taylor expanded in v around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. associate-*r* 97.0%

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

      3. neg-mul-1 97.0%

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

      4. distribute-rgt-out 97.0%

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

      5. unsub-neg 97.0%

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

   8. Simplified 97.0%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. associate-*r/ 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in m around inf 98.4%

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

       1. neg-mul-1 98.4%

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

       2. distribute-neg-frac2 98.4%

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

   13. Simplified 98.4%

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

4. Final simplification 97.7%

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

Alternative 7: 97.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := If[LessEqual[m, 1.0], N[(N[(N[(1.0 - m), $MachinePrecision] * N[(m - v), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision], N[(N[(m * N[(m * N[(m + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 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. 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* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in m around 0 97.0%

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

   6. Taylor expanded in v around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. associate-*r* 97.0%

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

      3. neg-mul-1 97.0%

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

      4. distribute-rgt-out 97.0%

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

      5. unsub-neg 97.0%

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

   8. Simplified 97.0%

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

   if 1 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in v around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. associate-*r/ 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in m around inf 98.4%

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

       1. neg-mul-1 98.4%

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

       2. distribute-neg-frac2 98.4%

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

   13. Simplified 98.4%

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

       1. associate-*r* 98.4%

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

       2. *-commutative 98.4%

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

       3. distribute-frac-neg2 98.4%

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

       4. distribute-frac-neg 98.4%

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

       5. associate-*r/ 98.4%

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

   15. Applied egg-rr 98.4%

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

4. Final simplification 97.8%

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

Alternative 8: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 9: 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* 99.8%

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

   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%

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

Alternative 10: 87.4% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.0)
		tmp = Float64(-1.0 + Float64(m / v));
	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 / v);
	else
		tmp = (m / v) * (m + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.0], N[(-1.0 + N[(m / v), $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 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* 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in m around 0 96.7%

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

      1. +-commutative 42.8%

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

      2. distribute-lft-in 42.8%

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

      3. div-inv 43.0%

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

      4. *-rgt-identity 43.0%

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

   7. Applied egg-rr 96.9%

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

   8. Taylor expanded in v around 0 96.9%

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

   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. 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 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. associate-*r/ 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in m around 0 0.1%

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

       1. associate-*r* 0.1%

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

       2. *-commutative 0.1%

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

       3. div-inv 0.1%

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

       4. frac-2neg 0.1%

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

       5. distribute-rgt-neg-in 0.1%

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

       6. add-sqr-sqrt 0.0%

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

       7. sqrt-unprod 84.2%

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

       8. sqr-neg 84.2%

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

       9. sqrt-unprod 84.2%

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

       10. add-sqr-sqrt 84.2%

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

   13. Applied egg-rr 84.2%

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

       1. associate-/l* 84.2%

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

       2. neg-sub0 84.2%

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

       3. associate--r- 84.2%

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

       4. metadata-eval 84.2%

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

       5. +-commutative 84.2%

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

       6. associate-*r/ 84.2%

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

       7. associate-*l/ 84.2%

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

   15. Simplified 84.2%

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

4. Final simplification 90.3%

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

Alternative 11: 61.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.05 \cdot 10^{-153}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;m + \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= m 2.05e-153) -1.0 (+ m (/ m v))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.05e-153) {
		tmp = -1.0;
	} else {
		tmp = m + (m / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 2.05d-153) then
        tmp = -1.0d0
    else
        tmp = m + (m / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 2.05e-153) {
		tmp = -1.0;
	} else {
		tmp = m + (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.05e-153:
		tmp = -1.0
	else:
		tmp = m + (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.05e-153)
		tmp = -1.0;
	else
		tmp = Float64(m + Float64(m / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.05e-153)
		tmp = -1.0;
	else
		tmp = m + (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.05e-153], -1.0, N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.05e-153

   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 80.6%

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

   if 2.05e-153 < 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* 99.8%

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

      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 70.0%

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

   6. Taylor expanded in m around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. distribute-lft-in 61.2%

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

      3. div-inv 61.3%

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

      4. *-rgt-identity 61.3%

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

   8. Applied egg-rr 61.3%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.05 \cdot 10^{-153}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;m + \frac{m}{v}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 26.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.2 \cdot 10^{-46}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= m 1.2e-46) -1.0 m))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.2e-46) {
		tmp = -1.0;
	} else {
		tmp = m;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.2d-46) then
        tmp = -1.0d0
    else
        tmp = m
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.2e-46) {
		tmp = -1.0;
	} else {
		tmp = m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.2e-46:
		tmp = -1.0
	else:
		tmp = m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.2e-46)
		tmp = -1.0;
	else
		tmp = m;
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.2e-46)
		tmp = -1.0;
	else
		tmp = m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.2e-46], -1.0, m]

Derivation

1. Split input into 2 regimes

2. if m < 1.20000000000000007e-46

   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 63.1%

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

   if 1.20000000000000007e-46 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-/l* 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in m around 0 62.3%

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

   6. Taylor expanded in m around inf 61.9%

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

   7. Taylor expanded in v around inf 5.5%

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

4. Final simplification 28.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.2 \cdot 10^{-46}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;m\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.5% accurate, 2.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := N[(-1.0 + N[(m / v), $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 77.1%

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

   1. +-commutative 51.2%

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

   2. distribute-lft-in 51.2%

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

   3. div-inv 51.3%

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

   4. *-rgt-identity 51.3%

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

7. Applied egg-rr 77.2%

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

8. Taylor expanded in v around 0 77.2%

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

9. Final simplification 77.2%

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

Alternative 14: 26.9% 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. neg-sub0 28.0%

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

   3. associate--r- 28.0%

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

   4. metadata-eval 28.0%

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

7. Simplified 28.0%

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

8. Final simplification 28.0%

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

Alternative 15: 24.5% 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 25.3%

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

6. Final simplification 25.3%

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

Reproduce

herbie shell --seed 2024067 
(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)))