b parameter of renormalized beta distribution

Percentage Accurate: 99.9% → 99.9%

Time: 5.6s

Alternatives: 13

Speedup: N/A×

• 41.3% 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

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

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 100.0%

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

   1. *-commutative 100.0%

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

   2. sub-neg 100.0%

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

   3. associate-*l/ 100.0%

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

   4. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 1.95 \cdot 10^{-15}:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(m - m \cdot m\right) \cdot \frac{1 - m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 1.95e-15) (+ -1.0 (+ m (/ m v))) (* (- m (* m m)) (/ (- 1.0 m) v))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.95e-15) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m - (m * m)) * ((1.0 - m) / v);
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 1.95d-15) then
        tmp = (-1.0d0) + (m + (m / v))
    else
        tmp = (m - (m * m)) * ((1.0d0 - m) / v)
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 1.95e-15) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m - (m * m)) * ((1.0 - m) / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 1.95e-15:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = (m - (m * m)) * ((1.0 - m) / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 1.95e-15)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(Float64(m - Float64(m * m)) * Float64(Float64(1.0 - m) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 1.95e-15)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = (m - (m * m)) * ((1.0 - m) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 1.95e-15], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m - N[(m * m), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 - m), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 1.95000000000000013e-15

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. +-commutative 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. *-lft-identity 99.8%

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

      7. associate-*l/ 100.0%

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

      8. *-lft-identity 100.0%

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

   6. Simplified 100.0%

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

   if 1.95000000000000013e-15 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. div-sub 55.1%

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

      2. clear-num 55.2%

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

      3. div-inv 55.1%

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

      4. clear-num 55.2%

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

   7. Applied egg-rr 55.2%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. unpow2 99.9%

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

   10. Simplified 99.9%

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

       1. associate-/l* 99.9%

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

       2. associate-/r/ 99.9%

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

   12. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 1.95 \cdot 10^{-15}:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(m - m \cdot m\right) \cdot \frac{1 - m}{v}\\ \end{array} \]

Alternative 3: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 7.7 \cdot 10^{-31}:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(1 - m\right) \cdot \left(m - m \cdot m\right)}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 7.7e-31) (+ -1.0 (+ m (/ m v))) (/ (* (- 1.0 m) (- m (* m m))) v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 7.7e-31) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = ((1.0 - m) * (m - (m * m))) / v;
	}
	return tmp;
}

Fortran

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    real(8) :: tmp
    if (m <= 7.7d-31) then
        tmp = (-1.0d0) + (m + (m / v))
    else
        tmp = ((1.0d0 - m) * (m - (m * m))) / v
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 7.7e-31) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = ((1.0 - m) * (m - (m * m))) / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 7.7e-31:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = ((1.0 - m) * (m - (m * m))) / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 7.7e-31)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(Float64(Float64(1.0 - m) * Float64(m - Float64(m * m))) / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 7.7e-31)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = ((1.0 - m) * (m - (m * m))) / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 7.7e-31], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - m), $MachinePrecision] * N[(m - N[(m * m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 7.70000000000000012e-31

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. +-commutative 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. *-lft-identity 99.8%

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

      7. associate-*l/ 100.0%

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

      8. *-lft-identity 100.0%

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

   6. Simplified 100.0%

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

   if 7.70000000000000012e-31 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. div-sub 56.4%

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

      2. clear-num 56.5%

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

      3. div-inv 56.4%

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

      4. clear-num 56.5%

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

   7. Applied egg-rr 56.5%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. unpow2 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 7.7 \cdot 10^{-31}:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(1 - m\right) \cdot \left(m - m \cdot m\right)}{v}\\ \end{array} \]

Alternative 4: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 7.7 \cdot 10^{-31}:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m + \left(m \cdot m\right) \cdot \left(m + -2\right)}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v)
 :precision binary64
 (if (<= m 7.7e-31) (+ -1.0 (+ m (/ m v))) (/ (+ m (* (* m m) (+ m -2.0))) v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 7.7e-31) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m + ((m * m) * (m + -2.0))) / 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 <= 7.7d-31) then
        tmp = (-1.0d0) + (m + (m / v))
    else
        tmp = (m + ((m * m) * (m + (-2.0d0)))) / v
    end if
    code = tmp
end function

Java

public static double code(double m, double v) {
	double tmp;
	if (m <= 7.7e-31) {
		tmp = -1.0 + (m + (m / v));
	} else {
		tmp = (m + ((m * m) * (m + -2.0))) / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 7.7e-31:
		tmp = -1.0 + (m + (m / v))
	else:
		tmp = (m + ((m * m) * (m + -2.0))) / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 7.7e-31)
		tmp = Float64(-1.0 + Float64(m + Float64(m / v)));
	else
		tmp = Float64(Float64(m + Float64(Float64(m * m) * Float64(m + -2.0))) / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 7.7e-31)
		tmp = -1.0 + (m + (m / v));
	else
		tmp = (m + ((m * m) * (m + -2.0))) / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 7.7e-31], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m + N[(N[(m * m), $MachinePrecision] * N[(m + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 7.70000000000000012e-31

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. +-commutative 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. *-lft-identity 99.8%

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

      7. associate-*l/ 100.0%

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

      8. *-lft-identity 100.0%

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

   6. Simplified 100.0%

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

   if 7.70000000000000012e-31 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. div-sub 56.4%

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

      2. clear-num 56.5%

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

      3. div-inv 56.4%

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

      4. clear-num 56.5%

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

   7. Applied egg-rr 56.5%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. unpow2 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in m around 0 58.7%

       \[\leadsto \frac{\color{blue}{-2 \cdot {m}^{2} + \left({m}^{3} + m\right)}}{v} \]
   12. Step-by-step derivation

       1. associate-+r+ 58.7%

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

       2. +-commutative 58.7%

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

       3. unpow2 58.7%

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

       4. cube-mult 58.6%

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

       5. distribute-rgt-out 99.9%

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

   13. Simplified 99.9%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 7.7 \cdot 10^{-31}:\\ \;\;\;\;-1 + \left(m + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{m + \left(m \cdot m\right) \cdot \left(m + -2\right)}{v}\\ \end{array} \]

Alternative 5: 98.2% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := If[LessEqual[m, 1.0], N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m + -1.0), $MachinePrecision] * N[(m * N[(m / v), $MachinePrecision]), $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/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 97.5%

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

      1. sub-neg 97.5%

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

      2. metadata-eval 97.5%

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

      3. +-commutative 97.5%

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

      4. *-commutative 97.5%

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

      5. distribute-rgt-in 97.5%

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

      6. *-lft-identity 97.5%

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

      7. associate-*l/ 97.7%

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

      8. *-lft-identity 97.7%

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

   6. Simplified 97.7%

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

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. unpow2 98.7%

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

   6. Simplified 98.7%

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

   7. Taylor expanded in v around 0 98.6%

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

      1. associate-*r/ 98.6%

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

      2. unpow2 98.6%

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

      3. *-commutative 98.6%

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

      4. associate-*r* 98.6%

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

      5. mul-1-neg 98.6%

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

      6. sub-neg 98.6%

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

      7. metadata-eval 98.6%

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

      8. distribute-neg-in 98.6%

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

      9. remove-double-neg 98.6%

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

      10. +-commutative 98.6%

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

   9. Simplified 98.6%

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

   10. Taylor expanded in m around 0 21.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{{m}^{2}}{v} + \frac{{m}^{3}}{v}} \]
   11. Step-by-step derivation

       1. +-commutative 21.4%

          \[\leadsto \color{blue}{\frac{{m}^{3}}{v} + -1 \cdot \frac{{m}^{2}}{v}} \]

       2. unpow2 21.4%

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

       3. neg-mul-1 21.4%

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

       4. unsub-neg 21.4%

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

       5. cube-mult 21.3%

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

       6. associate-/l* 21.3%

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

       7. *-lft-identity 21.3%

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

       8. associate-*l/ 21.3%

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

       9. associate-/r/ 21.3%

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

       10. div-sub 98.7%

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

       11. sub-neg 98.7%

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

       12. metadata-eval 98.7%

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

       13. associate-/l* 98.6%

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

       14. associate-*r/ 98.7%

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

       15. associate-*r/ 98.7%

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

   12. Simplified 98.7%

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

4. Final simplification 98.2%

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

Alternative 6: 98.2% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[m_, v_] := If[LessEqual[m, 1.0], N[(N[(1.0 - m), $MachinePrecision] * N[(N[(m / v), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(m + -1.0), $MachinePrecision] * N[(m * N[(m / v), $MachinePrecision]), $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/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 97.7%

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

   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%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. unpow2 98.7%

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

   6. Simplified 98.7%

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

   7. Taylor expanded in v around 0 98.6%

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

      1. associate-*r/ 98.6%

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

      2. unpow2 98.6%

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

      3. *-commutative 98.6%

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

      4. associate-*r* 98.6%

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

      5. mul-1-neg 98.6%

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

      6. sub-neg 98.6%

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

      7. metadata-eval 98.6%

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

      8. distribute-neg-in 98.6%

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

      9. remove-double-neg 98.6%

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

      10. +-commutative 98.6%

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

   9. Simplified 98.6%

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

   10. Taylor expanded in m around 0 21.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{{m}^{2}}{v} + \frac{{m}^{3}}{v}} \]
   11. Step-by-step derivation

       1. +-commutative 21.4%

          \[\leadsto \color{blue}{\frac{{m}^{3}}{v} + -1 \cdot \frac{{m}^{2}}{v}} \]

       2. unpow2 21.4%

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

       3. neg-mul-1 21.4%

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

       4. unsub-neg 21.4%

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

       5. cube-mult 21.3%

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

       6. associate-/l* 21.3%

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

       7. *-lft-identity 21.3%

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

       8. associate-*l/ 21.3%

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

       9. associate-/r/ 21.3%

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

       10. div-sub 98.7%

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

       11. sub-neg 98.7%

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

       12. metadata-eval 98.7%

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

       13. associate-/l* 98.6%

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

       14. associate-*r/ 98.7%

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

       15. associate-*r/ 98.7%

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

   12. Simplified 98.7%

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

4. Final simplification 98.2%

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

Alternative 7: 98.6% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double m, double v) {
	double tmp;
	if (m <= 1.6) {
		tmp = (1.0 - m) * ((m / v) + -1.0);
	} else {
		tmp = ((m * m) * (m + -2.0)) / 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 <= 1.6d0) then
        tmp = (1.0d0 - m) * ((m / v) + (-1.0d0))
    else
        tmp = ((m * m) * (m + (-2.0d0))) / v
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if m < 1.6000000000000001

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 97.7%

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

   if 1.6000000000000001 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. div-sub 53.1%

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

      2. clear-num 53.1%

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

      3. div-inv 53.0%

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

      4. clear-num 53.1%

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

   7. Applied egg-rr 53.1%

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

   8. Taylor expanded in v around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. unpow2 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in m around inf 54.7%

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

       1. unpow2 54.7%

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

       2. cube-mult 54.7%

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

       3. distribute-rgt-out 99.2%

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

   13. Simplified 99.2%

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

4. Final simplification 98.5%

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

Alternative 8: 62.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 7 \cdot 10^{-146}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;m + \frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= m 7e-146) -1.0 (+ m (/ m v))))

C

double code(double m, double v) {
	double tmp;
	if (m <= 7e-146) {
		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 <= 7d-146) 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 <= 7e-146) {
		tmp = -1.0;
	} else {
		tmp = m + (m / v);
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 7e-146:
		tmp = -1.0
	else:
		tmp = m + (m / v)
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 7e-146)
		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 <= 7e-146)
		tmp = -1.0;
	else
		tmp = m + (m / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 7e-146], -1.0, N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 7.0000000000000003e-146

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 74.1%

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

   if 7.0000000000000003e-146 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around 0 30.1%

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

   5. Taylor expanded in m around inf 24.4%

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

      1. +-commutative 24.4%

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

      2. *-commutative 24.4%

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

      3. mul-1-neg 24.4%

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

      4. unpow2 24.4%

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

      5. associate-*r/ 24.4%

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

      6. distribute-rgt-neg-in 24.4%

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

      7. distribute-lft-out 24.4%

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

      8. distribute-frac-neg 24.4%

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

   7. Simplified 24.4%

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

   8. Taylor expanded in m around 0 59.1%

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

   9. Taylor expanded in v around 0 59.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 7 \cdot 10^{-146}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;m + \frac{m}{v}\\ \end{array} \]

Alternative 9: 76.3% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. *-commutative 100.0%

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

   2. sub-neg 100.0%

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

   3. associate-*l/ 100.0%

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

   4. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in m around 0 74.1%

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

   1. sub-neg 74.1%

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

   2. metadata-eval 74.1%

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

   3. +-commutative 74.1%

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

   4. *-commutative 74.1%

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

   5. distribute-rgt-in 74.1%

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

   6. *-lft-identity 74.1%

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

   7. associate-*l/ 74.2%

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

   8. *-lft-identity 74.2%

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

6. Simplified 74.2%

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

7. Final simplification 74.2%

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

Alternative 10: 62.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.7 \cdot 10^{-146}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v}\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= m 2.7e-146) -1.0 (/ m v)))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.7e-146) {
		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 <= 2.7d-146) 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 <= 2.7e-146) {
		tmp = -1.0;
	} else {
		tmp = m / v;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.7e-146:
		tmp = -1.0
	else:
		tmp = m / v
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.7e-146)
		tmp = -1.0;
	else
		tmp = Float64(m / v);
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.7e-146)
		tmp = -1.0;
	else
		tmp = m / v;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.7e-146], -1.0, N[(m / v), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if m < 2.69999999999999995e-146

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 74.1%

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

   if 2.69999999999999995e-146 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. div-sub 67.7%

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

      2. clear-num 67.9%

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

      3. div-inv 67.8%

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

      4. clear-num 67.9%

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

   7. Applied egg-rr 67.9%

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

   8. Taylor expanded in v around 0 94.4%

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

      1. *-commutative 94.4%

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

      2. unpow2 94.4%

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

   10. Simplified 94.4%

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

   11. Taylor expanded in m around 0 59.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.7 \cdot 10^{-146}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v}\\ \end{array} \]

Alternative 11: 27.5% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 2.1 \cdot 10^{-49}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;m\\ \end{array} \end{array} \]

FPCore

(FPCore (m v) :precision binary64 (if (<= m 2.1e-49) -1.0 m))

C

double code(double m, double v) {
	double tmp;
	if (m <= 2.1e-49) {
		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 <= 2.1d-49) 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 <= 2.1e-49) {
		tmp = -1.0;
	} else {
		tmp = m;
	}
	return tmp;
}

Python

def code(m, v):
	tmp = 0
	if m <= 2.1e-49:
		tmp = -1.0
	else:
		tmp = m
	return tmp

Julia

function code(m, v)
	tmp = 0.0
	if (m <= 2.1e-49)
		tmp = -1.0;
	else
		tmp = m;
	end
	return tmp
end

MATLAB

function tmp_2 = code(m, v)
	tmp = 0.0;
	if (m <= 2.1e-49)
		tmp = -1.0;
	else
		tmp = m;
	end
	tmp_2 = tmp;
end

Wolfram

code[m_, v_] := If[LessEqual[m, 2.1e-49], -1.0, m]

Derivation

1. Split input into 2 regimes

2. if m < 2.0999999999999999e-49

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in m around 0 55.8%

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

   if 2.0999999999999999e-49 < m

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in m around 0 12.2%

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

   5. Taylor expanded in m around inf 11.8%

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

      1. +-commutative 11.8%

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

      2. *-commutative 11.8%

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

      3. mul-1-neg 11.8%

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

      4. unpow2 11.8%

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

      5. associate-*r/ 11.8%

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

      6. distribute-rgt-neg-in 11.8%

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

      7. distribute-lft-out 11.8%

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

      8. distribute-frac-neg 11.8%

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

   7. Simplified 11.8%

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

   8. Taylor expanded in v around inf 5.1%

      \[\leadsto m \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;m \leq 2.1 \cdot 10^{-49}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;m\\ \end{array} \]

Alternative 12: 27.7% 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 100.0%

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

   1. *-commutative 100.0%

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

   2. sub-neg 100.0%

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

   3. associate-*l/ 100.0%

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

   4. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in v around inf 26.0%

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

   1. neg-mul-1 26.0%

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

   2. neg-sub0 26.0%

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

   3. associate--r- 26.0%

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

   4. metadata-eval 26.0%

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

6. Simplified 26.0%

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

7. Final simplification 26.0%

   \[\leadsto m + -1 \]

Alternative 13: 25.3% 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 100.0%

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

   1. *-commutative 100.0%

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

   2. sub-neg 100.0%

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

   3. associate-*l/ 100.0%

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

   4. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in m around 0 23.8%

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

5. Final simplification 23.8%

   \[\leadsto -1 \]

Reproduce

herbie shell --seed 2023240 
(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)))