subtraction fraction

Percentage Accurate: 100.0% → 100.0%

Time: 8.2s

Alternatives: 8

Speedup: 1.1×

Specification

Math

\[\begin{array}{l} \\ \frac{-\left(f + n\right)}{f - n} \end{array} \]

FPCore

(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))

C

double code(double f, double n) {
	return -(f + n) / (f - n);
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    code = -(f + n) / (f - n)
end function

Java

public static double code(double f, double n) {
	return -(f + n) / (f - n);
}

Python

def code(f, n):
	return -(f + n) / (f - n)

Julia

function code(f, n)
	return Float64(Float64(-Float64(f + n)) / Float64(f - n))
end

MATLAB

function tmp = code(f, n)
	tmp = -(f + n) / (f - n);
end

Wolfram

code[f_, n_] := N[((-N[(f + n), $MachinePrecision]) / N[(f - n), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{-\left(f + n\right)}{f - n} \end{array} \]

FPCore

(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))

C

double code(double f, double n) {
	return -(f + n) / (f - n);
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    code = -(f + n) / (f - n)
end function

Java

public static double code(double f, double n) {
	return -(f + n) / (f - n);
}

Python

def code(f, n):
	return -(f + n) / (f - n)

Julia

function code(f, n)
	return Float64(Float64(-Float64(f + n)) / Float64(f - n))
end

MATLAB

function tmp = code(f, n)
	tmp = -(f + n) / (f - n);
end

Wolfram

code[f_, n_] := N[((-N[(f + n), $MachinePrecision]) / N[(f - n), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{f + n}{n - f} \end{array} \]

FPCore

(FPCore (f n) :precision binary64 (/ (+ f n) (- n f)))

C

double code(double f, double n) {
	return (f + n) / (n - f);
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    code = (f + n) / (n - f)
end function

Java

public static double code(double f, double n) {
	return (f + n) / (n - f);
}

Python

def code(f, n):
	return (f + n) / (n - f)

Julia

function code(f, n)
	return Float64(Float64(f + n) / Float64(n - f))
end

MATLAB

function tmp = code(f, n)
	tmp = (f + n) / (n - f);
end

Wolfram

code[f_, n_] := N[(N[(f + n), $MachinePrecision] / N[(n - f), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{-\left(f + n\right)}{f - n} \]
2. Step-by-step derivation

   1. distribute-frac-neg 99.9%

      \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

   2. distribute-neg-frac2 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

   3. sub-neg 99.9%

      \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

   4. +-commutative 99.9%

      \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

   5. distribute-neg-in 99.9%

      \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

   6. remove-double-neg 99.9%

      \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

   7. sub-neg 99.9%

      \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -8 \cdot 10^{-36} \lor \neg \left(n \leq 2.3 \cdot 10^{+27}\right):\\ \;\;\;\;1 + \frac{f \cdot 2}{n}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{n}{f} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (if (or (<= n -8e-36) (not (<= n 2.3e+27)))
   (+ 1.0 (/ (* f 2.0) n))
   (+ (* -2.0 (/ n f)) -1.0)))

C

double code(double f, double n) {
	double tmp;
	if ((n <= -8e-36) || !(n <= 2.3e+27)) {
		tmp = 1.0 + ((f * 2.0) / n);
	} else {
		tmp = (-2.0 * (n / f)) + -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    real(8) :: tmp
    if ((n <= (-8d-36)) .or. (.not. (n <= 2.3d+27))) then
        tmp = 1.0d0 + ((f * 2.0d0) / n)
    else
        tmp = ((-2.0d0) * (n / f)) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double f, double n) {
	double tmp;
	if ((n <= -8e-36) || !(n <= 2.3e+27)) {
		tmp = 1.0 + ((f * 2.0) / n);
	} else {
		tmp = (-2.0 * (n / f)) + -1.0;
	}
	return tmp;
}

Python

def code(f, n):
	tmp = 0
	if (n <= -8e-36) or not (n <= 2.3e+27):
		tmp = 1.0 + ((f * 2.0) / n)
	else:
		tmp = (-2.0 * (n / f)) + -1.0
	return tmp

Julia

function code(f, n)
	tmp = 0.0
	if ((n <= -8e-36) || !(n <= 2.3e+27))
		tmp = Float64(1.0 + Float64(Float64(f * 2.0) / n));
	else
		tmp = Float64(Float64(-2.0 * Float64(n / f)) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(f, n)
	tmp = 0.0;
	if ((n <= -8e-36) || ~((n <= 2.3e+27)))
		tmp = 1.0 + ((f * 2.0) / n);
	else
		tmp = (-2.0 * (n / f)) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[f_, n_] := If[Or[LessEqual[n, -8e-36], N[Not[LessEqual[n, 2.3e+27]], $MachinePrecision]], N[(1.0 + N[(N[(f * 2.0), $MachinePrecision] / n), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 * N[(n / f), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if n < -7.9999999999999995e-36 or 2.3000000000000001e27 < n

   1. Initial program 99.9%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.9%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in f around 0 74.6%

      \[\leadsto \color{blue}{1 + 2 \cdot \frac{f}{n}} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.6%

         \[\leadsto 1 + \color{blue}{\frac{2 \cdot f}{n}} \]

   7. Simplified 74.6%

      \[\leadsto \color{blue}{1 + \frac{2 \cdot f}{n}} \]

   if -7.9999999999999995e-36 < n < 2.3000000000000001e27

   1. Initial program 99.9%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.9%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in n around 0 78.6%

      \[\leadsto \color{blue}{-2 \cdot \frac{n}{f} - 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -8 \cdot 10^{-36} \lor \neg \left(n \leq 2.3 \cdot 10^{+27}\right):\\ \;\;\;\;1 + \frac{f \cdot 2}{n}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{n}{f} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -2.5 \cdot 10^{-36} \lor \neg \left(n \leq 2.1 \cdot 10^{+26}\right):\\ \;\;\;\;1 + \frac{f \cdot 2}{n}\\ \mathbf{else}:\\ \;\;\;\;\frac{f}{n - f}\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (if (or (<= n -2.5e-36) (not (<= n 2.1e+26)))
   (+ 1.0 (/ (* f 2.0) n))
   (/ f (- n f))))

C

double code(double f, double n) {
	double tmp;
	if ((n <= -2.5e-36) || !(n <= 2.1e+26)) {
		tmp = 1.0 + ((f * 2.0) / n);
	} else {
		tmp = f / (n - f);
	}
	return tmp;
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    real(8) :: tmp
    if ((n <= (-2.5d-36)) .or. (.not. (n <= 2.1d+26))) then
        tmp = 1.0d0 + ((f * 2.0d0) / n)
    else
        tmp = f / (n - f)
    end if
    code = tmp
end function

Java

public static double code(double f, double n) {
	double tmp;
	if ((n <= -2.5e-36) || !(n <= 2.1e+26)) {
		tmp = 1.0 + ((f * 2.0) / n);
	} else {
		tmp = f / (n - f);
	}
	return tmp;
}

Python

def code(f, n):
	tmp = 0
	if (n <= -2.5e-36) or not (n <= 2.1e+26):
		tmp = 1.0 + ((f * 2.0) / n)
	else:
		tmp = f / (n - f)
	return tmp

Julia

function code(f, n)
	tmp = 0.0
	if ((n <= -2.5e-36) || !(n <= 2.1e+26))
		tmp = Float64(1.0 + Float64(Float64(f * 2.0) / n));
	else
		tmp = Float64(f / Float64(n - f));
	end
	return tmp
end

MATLAB

function tmp_2 = code(f, n)
	tmp = 0.0;
	if ((n <= -2.5e-36) || ~((n <= 2.1e+26)))
		tmp = 1.0 + ((f * 2.0) / n);
	else
		tmp = f / (n - f);
	end
	tmp_2 = tmp;
end

Wolfram

code[f_, n_] := If[Or[LessEqual[n, -2.5e-36], N[Not[LessEqual[n, 2.1e+26]], $MachinePrecision]], N[(1.0 + N[(N[(f * 2.0), $MachinePrecision] / n), $MachinePrecision]), $MachinePrecision], N[(f / N[(n - f), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if n < -2.50000000000000002e-36 or 2.1000000000000001e26 < n

   1. Initial program 99.9%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.9%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in f around 0 74.6%

      \[\leadsto \color{blue}{1 + 2 \cdot \frac{f}{n}} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.6%

         \[\leadsto 1 + \color{blue}{\frac{2 \cdot f}{n}} \]

   7. Simplified 74.6%

      \[\leadsto \color{blue}{1 + \frac{2 \cdot f}{n}} \]

   if -2.50000000000000002e-36 < n < 2.1000000000000001e26

   1. Initial program 99.9%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.9%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in f around inf 78.3%

      \[\leadsto \frac{\color{blue}{f}}{n - f} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -2.5 \cdot 10^{-36} \lor \neg \left(n \leq 2.1 \cdot 10^{+26}\right):\\ \;\;\;\;1 + \frac{f \cdot 2}{n}\\ \mathbf{else}:\\ \;\;\;\;\frac{f}{n - f}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -5.3 \cdot 10^{-36} \lor \neg \left(n \leq 3.7 \cdot 10^{+28}\right):\\ \;\;\;\;1 + \frac{f}{n}\\ \mathbf{else}:\\ \;\;\;\;\frac{f}{n - f}\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (if (or (<= n -5.3e-36) (not (<= n 3.7e+28))) (+ 1.0 (/ f n)) (/ f (- n f))))

C

double code(double f, double n) {
	double tmp;
	if ((n <= -5.3e-36) || !(n <= 3.7e+28)) {
		tmp = 1.0 + (f / n);
	} else {
		tmp = f / (n - f);
	}
	return tmp;
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    real(8) :: tmp
    if ((n <= (-5.3d-36)) .or. (.not. (n <= 3.7d+28))) then
        tmp = 1.0d0 + (f / n)
    else
        tmp = f / (n - f)
    end if
    code = tmp
end function

Java

public static double code(double f, double n) {
	double tmp;
	if ((n <= -5.3e-36) || !(n <= 3.7e+28)) {
		tmp = 1.0 + (f / n);
	} else {
		tmp = f / (n - f);
	}
	return tmp;
}

Python

def code(f, n):
	tmp = 0
	if (n <= -5.3e-36) or not (n <= 3.7e+28):
		tmp = 1.0 + (f / n)
	else:
		tmp = f / (n - f)
	return tmp

Julia

function code(f, n)
	tmp = 0.0
	if ((n <= -5.3e-36) || !(n <= 3.7e+28))
		tmp = Float64(1.0 + Float64(f / n));
	else
		tmp = Float64(f / Float64(n - f));
	end
	return tmp
end

MATLAB

function tmp_2 = code(f, n)
	tmp = 0.0;
	if ((n <= -5.3e-36) || ~((n <= 3.7e+28)))
		tmp = 1.0 + (f / n);
	else
		tmp = f / (n - f);
	end
	tmp_2 = tmp;
end

Wolfram

code[f_, n_] := If[Or[LessEqual[n, -5.3e-36], N[Not[LessEqual[n, 3.7e+28]], $MachinePrecision]], N[(1.0 + N[(f / n), $MachinePrecision]), $MachinePrecision], N[(f / N[(n - f), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if n < -5.2999999999999998e-36 or 3.6999999999999999e28 < n

   1. Initial program 99.9%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.9%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in f around 0 73.5%

      \[\leadsto \frac{\color{blue}{n}}{n - f} \]

   6. Taylor expanded in n around inf 73.6%

      \[\leadsto \color{blue}{1 + \frac{f}{n}} \]

   if -5.2999999999999998e-36 < n < 3.6999999999999999e28

   1. Initial program 99.9%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.9%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in f around inf 78.3%

      \[\leadsto \frac{\color{blue}{f}}{n - f} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -5.3 \cdot 10^{-36} \lor \neg \left(n \leq 3.7 \cdot 10^{+28}\right):\\ \;\;\;\;1 + \frac{f}{n}\\ \mathbf{else}:\\ \;\;\;\;\frac{f}{n - f}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -1.95 \cdot 10^{-36} \lor \neg \left(n \leq 4 \cdot 10^{+28}\right):\\ \;\;\;\;1 + \frac{f}{n}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (if (or (<= n -1.95e-36) (not (<= n 4e+28))) (+ 1.0 (/ f n)) -1.0))

C

double code(double f, double n) {
	double tmp;
	if ((n <= -1.95e-36) || !(n <= 4e+28)) {
		tmp = 1.0 + (f / n);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    real(8) :: tmp
    if ((n <= (-1.95d-36)) .or. (.not. (n <= 4d+28))) then
        tmp = 1.0d0 + (f / n)
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double f, double n) {
	double tmp;
	if ((n <= -1.95e-36) || !(n <= 4e+28)) {
		tmp = 1.0 + (f / n);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(f, n):
	tmp = 0
	if (n <= -1.95e-36) or not (n <= 4e+28):
		tmp = 1.0 + (f / n)
	else:
		tmp = -1.0
	return tmp

Julia

function code(f, n)
	tmp = 0.0
	if ((n <= -1.95e-36) || !(n <= 4e+28))
		tmp = Float64(1.0 + Float64(f / n));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(f, n)
	tmp = 0.0;
	if ((n <= -1.95e-36) || ~((n <= 4e+28)))
		tmp = 1.0 + (f / n);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[f_, n_] := If[Or[LessEqual[n, -1.95e-36], N[Not[LessEqual[n, 4e+28]], $MachinePrecision]], N[(1.0 + N[(f / n), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if n < -1.95e-36 or 3.99999999999999983e28 < n

   1. Initial program 99.9%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.9%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in f around 0 73.5%

      \[\leadsto \frac{\color{blue}{n}}{n - f} \]

   6. Taylor expanded in n around inf 73.6%

      \[\leadsto \color{blue}{1 + \frac{f}{n}} \]

   if -1.95e-36 < n < 3.99999999999999983e28

   1. Initial program 99.9%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.9%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in f around inf 77.5%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -1.95 \cdot 10^{-36} \lor \neg \left(n \leq 4 \cdot 10^{+28}\right):\\ \;\;\;\;1 + \frac{f}{n}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -9.2 \cdot 10^{-39}:\\ \;\;\;\;1 + \frac{f}{n}\\ \mathbf{elif}\;n \leq 1.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{f}{n - f}\\ \mathbf{else}:\\ \;\;\;\;\frac{n}{n - f}\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (if (<= n -9.2e-39)
   (+ 1.0 (/ f n))
   (if (<= n 1.4e+26) (/ f (- n f)) (/ n (- n f)))))

C

double code(double f, double n) {
	double tmp;
	if (n <= -9.2e-39) {
		tmp = 1.0 + (f / n);
	} else if (n <= 1.4e+26) {
		tmp = f / (n - f);
	} else {
		tmp = n / (n - f);
	}
	return tmp;
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    real(8) :: tmp
    if (n <= (-9.2d-39)) then
        tmp = 1.0d0 + (f / n)
    else if (n <= 1.4d+26) then
        tmp = f / (n - f)
    else
        tmp = n / (n - f)
    end if
    code = tmp
end function

Java

public static double code(double f, double n) {
	double tmp;
	if (n <= -9.2e-39) {
		tmp = 1.0 + (f / n);
	} else if (n <= 1.4e+26) {
		tmp = f / (n - f);
	} else {
		tmp = n / (n - f);
	}
	return tmp;
}

Python

def code(f, n):
	tmp = 0
	if n <= -9.2e-39:
		tmp = 1.0 + (f / n)
	elif n <= 1.4e+26:
		tmp = f / (n - f)
	else:
		tmp = n / (n - f)
	return tmp

Julia

function code(f, n)
	tmp = 0.0
	if (n <= -9.2e-39)
		tmp = Float64(1.0 + Float64(f / n));
	elseif (n <= 1.4e+26)
		tmp = Float64(f / Float64(n - f));
	else
		tmp = Float64(n / Float64(n - f));
	end
	return tmp
end

MATLAB

function tmp_2 = code(f, n)
	tmp = 0.0;
	if (n <= -9.2e-39)
		tmp = 1.0 + (f / n);
	elseif (n <= 1.4e+26)
		tmp = f / (n - f);
	else
		tmp = n / (n - f);
	end
	tmp_2 = tmp;
end

Wolfram

code[f_, n_] := If[LessEqual[n, -9.2e-39], N[(1.0 + N[(f / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.4e+26], N[(f / N[(n - f), $MachinePrecision]), $MachinePrecision], N[(n / N[(n - f), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if n < -9.20000000000000033e-39

   1. Initial program 99.9%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.9%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in f around 0 71.6%

      \[\leadsto \frac{\color{blue}{n}}{n - f} \]

   6. Taylor expanded in n around inf 71.8%

      \[\leadsto \color{blue}{1 + \frac{f}{n}} \]

   if -9.20000000000000033e-39 < n < 1.4e26

   1. Initial program 99.9%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.9%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in f around inf 78.3%

      \[\leadsto \frac{\color{blue}{f}}{n - f} \]

   if 1.4e26 < n

   1. Initial program 99.8%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.8%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.8%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.8%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.8%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.8%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.8%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.8%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in f around 0 75.5%

      \[\leadsto \frac{\color{blue}{n}}{n - f} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -1 \cdot 10^{-35}:\\ \;\;\;\;1\\ \mathbf{elif}\;n \leq 2.5 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (if (<= n -1e-35) 1.0 (if (<= n 2.5e+27) -1.0 1.0)))

C

double code(double f, double n) {
	double tmp;
	if (n <= -1e-35) {
		tmp = 1.0;
	} else if (n <= 2.5e+27) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    real(8) :: tmp
    if (n <= (-1d-35)) then
        tmp = 1.0d0
    else if (n <= 2.5d+27) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double f, double n) {
	double tmp;
	if (n <= -1e-35) {
		tmp = 1.0;
	} else if (n <= 2.5e+27) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(f, n):
	tmp = 0
	if n <= -1e-35:
		tmp = 1.0
	elif n <= 2.5e+27:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(f, n)
	tmp = 0.0
	if (n <= -1e-35)
		tmp = 1.0;
	elseif (n <= 2.5e+27)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(f, n)
	tmp = 0.0;
	if (n <= -1e-35)
		tmp = 1.0;
	elseif (n <= 2.5e+27)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[f_, n_] := If[LessEqual[n, -1e-35], 1.0, If[LessEqual[n, 2.5e+27], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if n < -1.00000000000000001e-35 or 2.4999999999999999e27 < n

   1. Initial program 99.9%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.9%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in f around 0 72.8%

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

   if -1.00000000000000001e-35 < n < 2.4999999999999999e27

   1. Initial program 99.9%

      \[\frac{-\left(f + n\right)}{f - n} \]
   2. Step-by-step derivation

      1. distribute-frac-neg 99.9%

         \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

      3. sub-neg 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

      4. +-commutative 99.9%

         \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

      5. distribute-neg-in 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

      6. remove-double-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
   4. Add Preprocessing

   5. Taylor expanded in f around inf 77.5%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 49.5% accurate, 8.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (f n) :precision binary64 -1.0)

C

double code(double f, double n) {
	return -1.0;
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    code = -1.0d0
end function

Java

public static double code(double f, double n) {
	return -1.0;
}

Python

def code(f, n):
	return -1.0

Julia

function code(f, n)
	return -1.0
end

MATLAB

function tmp = code(f, n)
	tmp = -1.0;
end

Wolfram

code[f_, n_] := -1.0

Derivation

1. Initial program 99.9%

   \[\frac{-\left(f + n\right)}{f - n} \]
2. Step-by-step derivation

   1. distribute-frac-neg 99.9%

      \[\leadsto \color{blue}{-\frac{f + n}{f - n}} \]

   2. distribute-neg-frac2 99.9%

      \[\leadsto \color{blue}{\frac{f + n}{-\left(f - n\right)}} \]

   3. sub-neg 99.9%

      \[\leadsto \frac{f + n}{-\color{blue}{\left(f + \left(-n\right)\right)}} \]

   4. +-commutative 99.9%

      \[\leadsto \frac{f + n}{-\color{blue}{\left(\left(-n\right) + f\right)}} \]

   5. distribute-neg-in 99.9%

      \[\leadsto \frac{f + n}{\color{blue}{\left(-\left(-n\right)\right) + \left(-f\right)}} \]

   6. remove-double-neg 99.9%

      \[\leadsto \frac{f + n}{\color{blue}{n} + \left(-f\right)} \]

   7. sub-neg 99.9%

      \[\leadsto \frac{f + n}{\color{blue}{n - f}} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
4. Add Preprocessing

5. Taylor expanded in f around inf 52.5%

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

Reproduce

herbie shell --seed 2024110 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))