subtraction fraction

Percentage Accurate: 100.0% → 99.9%

Time: 8.6s

Alternatives: 6

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: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(f, n):
	return (((f + n) / (n - f)) + 1.0) + -1.0

Julia

function code(f, n)
	return Float64(Float64(Float64(Float64(f + n) / Float64(n - f)) + 1.0) + -1.0)
end

MATLAB

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

Wolfram

code[f_, n_] := N[(N[(N[(N[(f + n), $MachinePrecision] / N[(n - f), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + -1.0), $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. Step-by-step derivation

   1. expm1-log1p-u 96.8%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{f + n}{n - f}\right)\right)} \]

   2. expm1-undefine 96.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{f + n}{n - f}\right)} - 1} \]

6. Applied egg-rr 96.9%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{f + n}{n - f}\right)} - 1} \]
7. Step-by-step derivation

   1. log1p-undefine 96.9%

      \[\leadsto e^{\color{blue}{\log \left(1 + \frac{f + n}{n - f}\right)}} - 1 \]

   2. rem-exp-log 100.0%

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

   3. +-commutative 100.0%

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

8. Applied egg-rr 100.0%

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

9. Final simplification 100.0%

   \[\leadsto \left(\frac{f + n}{n - f} + 1\right) + -1 \]
10. Add Preprocessing

Alternative 2: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;f \leq -1.65 \cdot 10^{+39}:\\ \;\;\;\;-1\\ \mathbf{elif}\;f \leq -4.5 \cdot 10^{-7} \lor \neg \left(f \leq -9 \cdot 10^{-80}\right) \land f \leq 2.3 \cdot 10^{+27}:\\ \;\;\;\;1 + 2 \cdot \frac{f}{n}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (if (<= f -1.65e+39)
   -1.0
   (if (or (<= f -4.5e-7) (and (not (<= f -9e-80)) (<= f 2.3e+27)))
     (+ 1.0 (* 2.0 (/ f n)))
     -1.0)))

C

double code(double f, double n) {
	double tmp;
	if (f <= -1.65e+39) {
		tmp = -1.0;
	} else if ((f <= -4.5e-7) || (!(f <= -9e-80) && (f <= 2.3e+27))) {
		tmp = 1.0 + (2.0 * (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 (f <= (-1.65d+39)) then
        tmp = -1.0d0
    else if ((f <= (-4.5d-7)) .or. (.not. (f <= (-9d-80))) .and. (f <= 2.3d+27)) then
        tmp = 1.0d0 + (2.0d0 * (f / n))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double f, double n) {
	double tmp;
	if (f <= -1.65e+39) {
		tmp = -1.0;
	} else if ((f <= -4.5e-7) || (!(f <= -9e-80) && (f <= 2.3e+27))) {
		tmp = 1.0 + (2.0 * (f / n));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(f, n):
	tmp = 0
	if f <= -1.65e+39:
		tmp = -1.0
	elif (f <= -4.5e-7) or (not (f <= -9e-80) and (f <= 2.3e+27)):
		tmp = 1.0 + (2.0 * (f / n))
	else:
		tmp = -1.0
	return tmp

Julia

function code(f, n)
	tmp = 0.0
	if (f <= -1.65e+39)
		tmp = -1.0;
	elseif ((f <= -4.5e-7) || (!(f <= -9e-80) && (f <= 2.3e+27)))
		tmp = Float64(1.0 + Float64(2.0 * Float64(f / n)));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(f, n)
	tmp = 0.0;
	if (f <= -1.65e+39)
		tmp = -1.0;
	elseif ((f <= -4.5e-7) || (~((f <= -9e-80)) && (f <= 2.3e+27)))
		tmp = 1.0 + (2.0 * (f / n));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[f_, n_] := If[LessEqual[f, -1.65e+39], -1.0, If[Or[LessEqual[f, -4.5e-7], And[N[Not[LessEqual[f, -9e-80]], $MachinePrecision], LessEqual[f, 2.3e+27]]], N[(1.0 + N[(2.0 * N[(f / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if f < -1.6500000000000001e39 or -4.4999999999999998e-7 < f < -9.0000000000000006e-80 or 2.3000000000000001e27 < f

   1. Initial program 100.0%

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

      1. distribute-frac-neg 100.0%

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

      2. distribute-neg-frac2 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. remove-double-neg 100.0%

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

      7. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in f around inf 84.2%

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

   if -1.6500000000000001e39 < f < -4.4999999999999998e-7 or -9.0000000000000006e-80 < f < 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 f around 0 73.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;f \leq -1.65 \cdot 10^{+39}:\\ \;\;\;\;-1\\ \mathbf{elif}\;f \leq -4.5 \cdot 10^{-7} \lor \neg \left(f \leq -9 \cdot 10^{-80}\right) \land f \leq 2.3 \cdot 10^{+27}:\\ \;\;\;\;1 + 2 \cdot \frac{f}{n}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -2 \cdot \frac{n}{f} + -1\\ t_1 := 1 + 2 \cdot \frac{f}{n}\\ \mathbf{if}\;f \leq -4.2 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;f \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;f \leq -1.3 \cdot 10^{-79}:\\ \;\;\;\;-1\\ \mathbf{elif}\;f \leq 6.5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (let* ((t_0 (+ (* -2.0 (/ n f)) -1.0)) (t_1 (+ 1.0 (* 2.0 (/ f n)))))
   (if (<= f -4.2e+33)
     t_0
     (if (<= f -1.18e-6)
       t_1
       (if (<= f -1.3e-79) -1.0 (if (<= f 6.5e+25) t_1 t_0))))))

C

double code(double f, double n) {
	double t_0 = (-2.0 * (n / f)) + -1.0;
	double t_1 = 1.0 + (2.0 * (f / n));
	double tmp;
	if (f <= -4.2e+33) {
		tmp = t_0;
	} else if (f <= -1.18e-6) {
		tmp = t_1;
	} else if (f <= -1.3e-79) {
		tmp = -1.0;
	} else if (f <= 6.5e+25) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((-2.0d0) * (n / f)) + (-1.0d0)
    t_1 = 1.0d0 + (2.0d0 * (f / n))
    if (f <= (-4.2d+33)) then
        tmp = t_0
    else if (f <= (-1.18d-6)) then
        tmp = t_1
    else if (f <= (-1.3d-79)) then
        tmp = -1.0d0
    else if (f <= 6.5d+25) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double f, double n) {
	double t_0 = (-2.0 * (n / f)) + -1.0;
	double t_1 = 1.0 + (2.0 * (f / n));
	double tmp;
	if (f <= -4.2e+33) {
		tmp = t_0;
	} else if (f <= -1.18e-6) {
		tmp = t_1;
	} else if (f <= -1.3e-79) {
		tmp = -1.0;
	} else if (f <= 6.5e+25) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(f, n):
	t_0 = (-2.0 * (n / f)) + -1.0
	t_1 = 1.0 + (2.0 * (f / n))
	tmp = 0
	if f <= -4.2e+33:
		tmp = t_0
	elif f <= -1.18e-6:
		tmp = t_1
	elif f <= -1.3e-79:
		tmp = -1.0
	elif f <= 6.5e+25:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(f, n)
	t_0 = Float64(Float64(-2.0 * Float64(n / f)) + -1.0)
	t_1 = Float64(1.0 + Float64(2.0 * Float64(f / n)))
	tmp = 0.0
	if (f <= -4.2e+33)
		tmp = t_0;
	elseif (f <= -1.18e-6)
		tmp = t_1;
	elseif (f <= -1.3e-79)
		tmp = -1.0;
	elseif (f <= 6.5e+25)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(f, n)
	t_0 = (-2.0 * (n / f)) + -1.0;
	t_1 = 1.0 + (2.0 * (f / n));
	tmp = 0.0;
	if (f <= -4.2e+33)
		tmp = t_0;
	elseif (f <= -1.18e-6)
		tmp = t_1;
	elseif (f <= -1.3e-79)
		tmp = -1.0;
	elseif (f <= 6.5e+25)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[f_, n_] := Block[{t$95$0 = N[(N[(-2.0 * N[(n / f), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(2.0 * N[(f / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[f, -4.2e+33], t$95$0, If[LessEqual[f, -1.18e-6], t$95$1, If[LessEqual[f, -1.3e-79], -1.0, If[LessEqual[f, 6.5e+25], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if f < -4.2000000000000001e33 or 6.50000000000000005e25 < f

   1. Initial program 100.0%

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

      1. distribute-frac-neg 100.0%

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

      2. distribute-neg-frac2 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. remove-double-neg 100.0%

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

      7. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in n around 0 84.1%

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

   if -4.2000000000000001e33 < f < -1.17999999999999993e-6 or -1.29999999999999997e-79 < f < 6.50000000000000005e25

   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 73.8%

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

   if -1.17999999999999993e-6 < f < -1.29999999999999997e-79

   1. Initial program 100.0%

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

      1. distribute-frac-neg 100.0%

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

      2. distribute-neg-frac2 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. remove-double-neg 100.0%

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

      7. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in f around inf 100.0%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;f \leq -4.2 \cdot 10^{+33}:\\ \;\;\;\;-2 \cdot \frac{n}{f} + -1\\ \mathbf{elif}\;f \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;1 + 2 \cdot \frac{f}{n}\\ \mathbf{elif}\;f \leq -1.3 \cdot 10^{-79}:\\ \;\;\;\;-1\\ \mathbf{elif}\;f \leq 6.5 \cdot 10^{+25}:\\ \;\;\;\;1 + 2 \cdot \frac{f}{n}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{n}{f} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;f \leq -1 \cdot 10^{+38}:\\ \;\;\;\;-1\\ \mathbf{elif}\;f \leq -100000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;f \leq -1.85 \cdot 10^{-115}:\\ \;\;\;\;-1\\ \mathbf{elif}\;f \leq 6.2 \cdot 10^{+25}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (if (<= f -1e+38)
   -1.0
   (if (<= f -100000000000.0)
     1.0
     (if (<= f -1.85e-115) -1.0 (if (<= f 6.2e+25) 1.0 -1.0)))))

C

double code(double f, double n) {
	double tmp;
	if (f <= -1e+38) {
		tmp = -1.0;
	} else if (f <= -100000000000.0) {
		tmp = 1.0;
	} else if (f <= -1.85e-115) {
		tmp = -1.0;
	} else if (f <= 6.2e+25) {
		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 (f <= (-1d+38)) then
        tmp = -1.0d0
    else if (f <= (-100000000000.0d0)) then
        tmp = 1.0d0
    else if (f <= (-1.85d-115)) then
        tmp = -1.0d0
    else if (f <= 6.2d+25) 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 (f <= -1e+38) {
		tmp = -1.0;
	} else if (f <= -100000000000.0) {
		tmp = 1.0;
	} else if (f <= -1.85e-115) {
		tmp = -1.0;
	} else if (f <= 6.2e+25) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(f, n):
	tmp = 0
	if f <= -1e+38:
		tmp = -1.0
	elif f <= -100000000000.0:
		tmp = 1.0
	elif f <= -1.85e-115:
		tmp = -1.0
	elif f <= 6.2e+25:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(f, n)
	tmp = 0.0
	if (f <= -1e+38)
		tmp = -1.0;
	elseif (f <= -100000000000.0)
		tmp = 1.0;
	elseif (f <= -1.85e-115)
		tmp = -1.0;
	elseif (f <= 6.2e+25)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(f, n)
	tmp = 0.0;
	if (f <= -1e+38)
		tmp = -1.0;
	elseif (f <= -100000000000.0)
		tmp = 1.0;
	elseif (f <= -1.85e-115)
		tmp = -1.0;
	elseif (f <= 6.2e+25)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[f_, n_] := If[LessEqual[f, -1e+38], -1.0, If[LessEqual[f, -100000000000.0], 1.0, If[LessEqual[f, -1.85e-115], -1.0, If[LessEqual[f, 6.2e+25], 1.0, -1.0]]]]

Derivation

1. Split input into 2 regimes

2. if f < -9.99999999999999977e37 or -1e11 < f < -1.85e-115 or 6.1999999999999996e25 < f

   1. Initial program 100.0%

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

      1. distribute-frac-neg 100.0%

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

      2. distribute-neg-frac2 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. remove-double-neg 100.0%

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

      7. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in f around inf 81.0%

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

   if -9.99999999999999977e37 < f < -1e11 or -1.85e-115 < f < 6.1999999999999996e25

   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 76.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;f \leq -1 \cdot 10^{+38}:\\ \;\;\;\;-1\\ \mathbf{elif}\;f \leq -100000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;f \leq -1.85 \cdot 10^{-115}:\\ \;\;\;\;-1\\ \mathbf{elif}\;f \leq 6.2 \cdot 10^{+25}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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. Final simplification 99.9%

   \[\leadsto \frac{f + n}{n - f} \]
6. Add Preprocessing

Alternative 6: 50.0% 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 56.3%

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

6. Final simplification 56.3%

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

Reproduce

herbie shell --seed 2024055 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))