subtraction fraction

Percentage Accurate: 100.0% → 100.0%

Time: 6.6s

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: 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 100.0%

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

   1. lift-/.f64 N/A

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

   2. lift-neg.f64 N/A

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

   3. distribute-frac-neg N/A

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

   4. distribute-frac-neg2 N/A

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

   5. lower-/.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. +-commutative N/A

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

   8. lower-+.f64 N/A

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

   9. lift--.f64 N/A

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

   10. sub-neg N/A

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

   11. +-commutative N/A

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

   12. distribute-neg-in N/A

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

   13. remove-double-neg N/A

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

   14. sub-neg N/A

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

   15. lower--.f64 100.0

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

4. Applied rewrites 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{f + n}{n - f} \leq -0.5:\\ \;\;\;\;\mathsf{fma}\left(\frac{-2}{f}, n, -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-n}{f - n}\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (if (<= (/ (+ f n) (- n f)) -0.5) (fma (/ -2.0 f) n -1.0) (/ (- n) (- f n))))

C

double code(double f, double n) {
	double tmp;
	if (((f + n) / (n - f)) <= -0.5) {
		tmp = fma((-2.0 / f), n, -1.0);
	} else {
		tmp = -n / (f - n);
	}
	return tmp;
}

Julia

function code(f, n)
	tmp = 0.0
	if (Float64(Float64(f + n) / Float64(n - f)) <= -0.5)
		tmp = fma(Float64(-2.0 / f), n, -1.0);
	else
		tmp = Float64(Float64(-n) / Float64(f - n));
	end
	return tmp
end

Wolfram

code[f_, n_] := If[LessEqual[N[(N[(f + n), $MachinePrecision] / N[(n - f), $MachinePrecision]), $MachinePrecision], -0.5], N[(N[(-2.0 / f), $MachinePrecision] * n + -1.0), $MachinePrecision], N[((-n) / N[(f - n), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n)) < -0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in f around inf

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. distribute-neg-frac2 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. distribute-rgt1-in N/A

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

      7. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{2} \cdot n}{\mathsf{neg}\left(f\right)} + \left(\mathsf{neg}\left(1\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \frac{2 \cdot n}{\color{blue}{-1 \cdot f}} + \left(\mathsf{neg}\left(1\right)\right) \]

      9. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{2}{-1 \cdot f} \cdot n} + \left(\mathsf{neg}\left(1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \frac{2}{\color{blue}{\mathsf{neg}\left(f\right)}} \cdot n + \left(\mathsf{neg}\left(1\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{2}{f}\right)\right)} \cdot n + \left(\mathsf{neg}\left(1\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(\mathsf{neg}\left(\frac{\color{blue}{2 \cdot 1}}{f}\right)\right) \cdot n + \left(\mathsf{neg}\left(1\right)\right) \]

      13. associate-*r/ N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{2 \cdot \frac{1}{f}}\right)\right) \cdot n + \left(\mathsf{neg}\left(1\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \left(\mathsf{neg}\left(2 \cdot \frac{1}{f}\right)\right) \cdot n + \color{blue}{-1} \]

      15. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(2 \cdot \frac{1}{f}\right), n, -1\right)} \]

      16. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\frac{2 \cdot 1}{f}}\right), n, -1\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\frac{\color{blue}{2}}{f}\right), n, -1\right) \]

      18. distribute-neg-frac N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\mathsf{neg}\left(2\right)}{f}}, n, -1\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-2}}{f}, n, -1\right) \]

      20. lower-/.f64 99.0

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-2}{f}}, n, -1\right) \]

   5. Applied rewrites 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-2}{f}, n, -1\right)} \]

   if -0.5 < (/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))

   1. Initial program 100.0%

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

   3. Taylor expanded in f around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 97.6

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

   5. Applied rewrites 97.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{f + n}{n - f} \leq -0.5:\\ \;\;\;\;\mathsf{fma}\left(\frac{-2}{f}, n, -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-n}{f - n}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{f + n}{n - f} \leq -0.5:\\ \;\;\;\;\frac{-f}{f - n}\\ \mathbf{else}:\\ \;\;\;\;\frac{-n}{f - n}\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (if (<= (/ (+ f n) (- n f)) -0.5) (/ (- f) (- f n)) (/ (- n) (- f n))))

C

double code(double f, double n) {
	double tmp;
	if (((f + n) / (n - f)) <= -0.5) {
		tmp = -f / (f - n);
	} else {
		tmp = -n / (f - n);
	}
	return tmp;
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    real(8) :: tmp
    if (((f + n) / (n - f)) <= (-0.5d0)) then
        tmp = -f / (f - n)
    else
        tmp = -n / (f - n)
    end if
    code = tmp
end function

Java

public static double code(double f, double n) {
	double tmp;
	if (((f + n) / (n - f)) <= -0.5) {
		tmp = -f / (f - n);
	} else {
		tmp = -n / (f - n);
	}
	return tmp;
}

Python

def code(f, n):
	tmp = 0
	if ((f + n) / (n - f)) <= -0.5:
		tmp = -f / (f - n)
	else:
		tmp = -n / (f - n)
	return tmp

Julia

function code(f, n)
	tmp = 0.0
	if (Float64(Float64(f + n) / Float64(n - f)) <= -0.5)
		tmp = Float64(Float64(-f) / Float64(f - n));
	else
		tmp = Float64(Float64(-n) / Float64(f - n));
	end
	return tmp
end

MATLAB

function tmp_2 = code(f, n)
	tmp = 0.0;
	if (((f + n) / (n - f)) <= -0.5)
		tmp = -f / (f - n);
	else
		tmp = -n / (f - n);
	end
	tmp_2 = tmp;
end

Wolfram

code[f_, n_] := If[LessEqual[N[(N[(f + n), $MachinePrecision] / N[(n - f), $MachinePrecision]), $MachinePrecision], -0.5], N[((-f) / N[(f - n), $MachinePrecision]), $MachinePrecision], N[((-n) / N[(f - n), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n)) < -0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in f around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 98.2

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

   5. Applied rewrites 98.2%

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

   if -0.5 < (/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))

   1. Initial program 100.0%

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

   3. Taylor expanded in f around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 97.6

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

   5. Applied rewrites 97.6%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{f + n}{n - f} \leq -0.5:\\ \;\;\;\;\frac{-f}{f - n}\\ \mathbf{else}:\\ \;\;\;\;\frac{-n}{f - n}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{f + n}{n - f} \leq -0.5:\\ \;\;\;\;\frac{-f}{f - n}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (if (<= (/ (+ f n) (- n f)) -0.5) (/ (- f) (- f n)) 1.0))

C

double code(double f, double n) {
	double tmp;
	if (((f + n) / (n - f)) <= -0.5) {
		tmp = -f / (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 + n) / (n - f)) <= (-0.5d0)) then
        tmp = -f / (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 + n) / (n - f)) <= -0.5) {
		tmp = -f / (f - n);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(f, n):
	tmp = 0
	if ((f + n) / (n - f)) <= -0.5:
		tmp = -f / (f - n)
	else:
		tmp = 1.0
	return tmp

Julia

function code(f, n)
	tmp = 0.0
	if (Float64(Float64(f + n) / Float64(n - f)) <= -0.5)
		tmp = Float64(Float64(-f) / Float64(f - n));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(f, n)
	tmp = 0.0;
	if (((f + n) / (n - f)) <= -0.5)
		tmp = -f / (f - n);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[f_, n_] := If[LessEqual[N[(N[(f + n), $MachinePrecision] / N[(n - f), $MachinePrecision]), $MachinePrecision], -0.5], N[((-f) / N[(f - n), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n)) < -0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in f around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 98.2

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

   5. Applied rewrites 98.2%

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

   if -0.5 < (/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))

   1. Initial program 100.0%

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

   3. Taylor expanded in f around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.5%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{f + n}{n - f} \leq -0.5:\\ \;\;\;\;\frac{-f}{f - n}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{f + n}{n - f} \leq -5 \cdot 10^{-310}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (f n)
 :precision binary64
 (if (<= (/ (+ f n) (- n f)) -5e-310) -1.0 1.0))

C

double code(double f, double n) {
	double tmp;
	if (((f + n) / (n - f)) <= -5e-310) {
		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 + n) / (n - f)) <= (-5d-310)) 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 + n) / (n - f)) <= -5e-310) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(f, n):
	tmp = 0
	if ((f + n) / (n - f)) <= -5e-310:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(f, n)
	tmp = 0.0
	if (Float64(Float64(f + n) / Float64(n - f)) <= -5e-310)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(f, n)
	tmp = 0.0;
	if (((f + n) / (n - f)) <= -5e-310)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[f_, n_] := If[LessEqual[N[(N[(f + n), $MachinePrecision] / N[(n - f), $MachinePrecision]), $MachinePrecision], -5e-310], -1.0, 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n)) < -4.999999999999985e-310

   1. Initial program 100.0%

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

   3. Taylor expanded in f around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.1%

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

   if -4.999999999999985e-310 < (/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))

   1. Initial program 100.0%

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

   3. Taylor expanded in f around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.5%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{f + n}{n - f} \leq -5 \cdot 10^{-310}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.8% accurate, 20.0× 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 100.0%

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

3. Taylor expanded in f around inf

   \[\leadsto \color{blue}{-1} \]
4. Step-by-step derivation

5. Applied rewrites 45.3%

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

Reproduce

herbie shell --seed 2024277 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))