Asymptote C

Percentage Accurate: 53.5% → 100.0%

Time: 6.5s

Alternatives: 9

Speedup: 1.8×

Specification

Math

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

FPCore

(FPCore (x) :precision binary64 (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))

C

double code(double x) {
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
}

Fortran

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

Java

public static double code(double x) {
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
}

Python

def code(x):
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0))

Julia

function code(x)
	return Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / Float64(x - 1.0)))
end

MATLAB

function tmp = code(x)
	tmp = (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
end

Wolfram

code[x_] := N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 53.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))

C

double code(double x) {
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
}

Fortran

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

Java

public static double code(double x) {
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
}

Python

def code(x):
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0))

Julia

function code(x)
	return Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / Float64(x - 1.0)))
end

MATLAB

function tmp = code(x)
	tmp = (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
end

Wolfram

code[x_] := N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{x + 1} \cdot -3 + \frac{-1}{x + 1}}{x + -1} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ (+ (* (/ x (+ x 1.0)) -3.0) (/ -1.0 (+ x 1.0))) (+ x -1.0)))

C

double code(double x) {
	return (((x / (x + 1.0)) * -3.0) + (-1.0 / (x + 1.0))) / (x + -1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (((x / (x + 1.0d0)) * (-3.0d0)) + ((-1.0d0) / (x + 1.0d0))) / (x + (-1.0d0))
end function

Java

public static double code(double x) {
	return (((x / (x + 1.0)) * -3.0) + (-1.0 / (x + 1.0))) / (x + -1.0);
}

Python

def code(x):
	return (((x / (x + 1.0)) * -3.0) + (-1.0 / (x + 1.0))) / (x + -1.0)

Julia

function code(x)
	return Float64(Float64(Float64(Float64(x / Float64(x + 1.0)) * -3.0) + Float64(-1.0 / Float64(x + 1.0))) / Float64(x + -1.0))
end

MATLAB

function tmp = code(x)
	tmp = (((x / (x + 1.0)) * -3.0) + (-1.0 / (x + 1.0))) / (x + -1.0);
end

Wolfram

code[x_] := N[(N[(N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * -3.0), $MachinePrecision] + N[(-1.0 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 56.6%

   \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
2. Step-by-step derivation

   1. frac-sub 54.9%

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

   2. associate-/r* 54.9%

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

   3. sub-neg 54.9%

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

   4. distribute-rgt-in 54.9%

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

   5. metadata-eval 54.9%

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

   6. neg-mul-1 54.9%

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

   7. fma-def 54.9%

      \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(x, x, -x\right)} - \left(x + 1\right) \cdot \left(x + 1\right)}{x + 1}}{x - 1} \]

   8. fma-neg 54.9%

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

   9. pow2 54.9%

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

   10. sub-neg 54.9%

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

   11. metadata-eval 54.9%

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

3. Applied egg-rr 54.9%

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

4. Taylor expanded in x around 0 99.8%

   \[\leadsto \frac{\frac{\color{blue}{-3 \cdot x - 1}}{x + 1}}{x + -1} \]
5. Step-by-step derivation

   1. div-sub 99.8%

      \[\leadsto \frac{\color{blue}{\frac{-3 \cdot x}{x + 1} - \frac{1}{x + 1}}}{x + -1} \]

   2. sub-neg 99.8%

      \[\leadsto \frac{\color{blue}{\frac{-3 \cdot x}{x + 1} + \left(-\frac{1}{x + 1}\right)}}{x + -1} \]

6. Applied egg-rr 99.8%

   \[\leadsto \frac{\color{blue}{\frac{-3 \cdot x}{x + 1} + \left(-\frac{1}{x + 1}\right)}}{x + -1} \]
7. Step-by-step derivation

   1. *-commutative 99.8%

      \[\leadsto \frac{\frac{\color{blue}{x \cdot -3}}{x + 1} + \left(-\frac{1}{x + 1}\right)}{x + -1} \]

   2. associate-/l* 100.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{\frac{x + 1}{-3}}} + \left(-\frac{1}{x + 1}\right)}{x + -1} \]

   3. distribute-neg-frac 100.0%

      \[\leadsto \frac{\frac{x}{\frac{x + 1}{-3}} + \color{blue}{\frac{-1}{x + 1}}}{x + -1} \]

   4. metadata-eval 100.0%

      \[\leadsto \frac{\frac{x}{\frac{x + 1}{-3}} + \frac{\color{blue}{-1}}{x + 1}}{x + -1} \]

8. Simplified 100.0%

   \[\leadsto \frac{\color{blue}{\frac{x}{\frac{x + 1}{-3}} + \frac{-1}{x + 1}}}{x + -1} \]
9. Step-by-step derivation

   1. associate-/r/ 100.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{x + 1} \cdot -3} + \frac{-1}{x + 1}}{x + -1} \]

10. Applied egg-rr 100.0%

    \[\leadsto \frac{\color{blue}{\frac{x}{x + 1} \cdot -3} + \frac{-1}{x + 1}}{x + -1} \]

11. Final simplification 100.0%

    \[\leadsto \frac{\frac{x}{x + 1} \cdot -3 + \frac{-1}{x + 1}}{x + -1} \]

Alternative 2: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + 1} + \frac{-1 - x}{x + -1}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\frac{-3}{x} + \frac{\frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (+ (/ x (+ x 1.0)) (/ (- -1.0 x) (+ x -1.0)))))
   (if (<= t_0 5e-11) (+ (/ -3.0 x) (/ (/ -1.0 x) x)) t_0)))

C

double code(double x) {
	double t_0 = (x / (x + 1.0)) + ((-1.0 - x) / (x + -1.0));
	double tmp;
	if (t_0 <= 5e-11) {
		tmp = (-3.0 / x) + ((-1.0 / x) / x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x / (x + 1.0d0)) + (((-1.0d0) - x) / (x + (-1.0d0)))
    if (t_0 <= 5d-11) then
        tmp = ((-3.0d0) / x) + (((-1.0d0) / x) / x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = (x / (x + 1.0)) + ((-1.0 - x) / (x + -1.0));
	double tmp;
	if (t_0 <= 5e-11) {
		tmp = (-3.0 / x) + ((-1.0 / x) / x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = (x / (x + 1.0)) + ((-1.0 - x) / (x + -1.0))
	tmp = 0
	if t_0 <= 5e-11:
		tmp = (-3.0 / x) + ((-1.0 / x) / x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(-1.0 - x) / Float64(x + -1.0)))
	tmp = 0.0
	if (t_0 <= 5e-11)
		tmp = Float64(Float64(-3.0 / x) + Float64(Float64(-1.0 / x) / x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = (x / (x + 1.0)) + ((-1.0 - x) / (x + -1.0));
	tmp = 0.0;
	if (t_0 <= 5e-11)
		tmp = (-3.0 / x) + ((-1.0 / x) / x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 - x), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e-11], N[(N[(-3.0 / x), $MachinePrecision] + N[(N[(-1.0 / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) < 5.00000000000000018e-11

   1. Initial program 8.3%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]

   2. Taylor expanded in x around inf 98.8%

      \[\leadsto \color{blue}{-\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right)} \]
   3. Step-by-step derivation

      1. +-commutative 98.8%

         \[\leadsto -\color{blue}{\left(3 \cdot \frac{1}{x} + \frac{1}{{x}^{2}}\right)} \]

      2. distribute-neg-in 98.8%

         \[\leadsto \color{blue}{\left(-3 \cdot \frac{1}{x}\right) + \left(-\frac{1}{{x}^{2}}\right)} \]

      3. sub-neg 98.8%

         \[\leadsto \color{blue}{\left(-3 \cdot \frac{1}{x}\right) - \frac{1}{{x}^{2}}} \]

      4. associate-*r/ 99.3%

         \[\leadsto \left(-\color{blue}{\frac{3 \cdot 1}{x}}\right) - \frac{1}{{x}^{2}} \]

      5. metadata-eval 99.3%

         \[\leadsto \left(-\frac{\color{blue}{3}}{x}\right) - \frac{1}{{x}^{2}} \]

      6. distribute-neg-frac 99.3%

         \[\leadsto \color{blue}{\frac{-3}{x}} - \frac{1}{{x}^{2}} \]

      7. metadata-eval 99.3%

         \[\leadsto \frac{\color{blue}{-3}}{x} - \frac{1}{{x}^{2}} \]

      8. unpow2 99.3%

         \[\leadsto \frac{-3}{x} - \frac{1}{\color{blue}{x \cdot x}} \]

      9. associate-/r* 99.3%

         \[\leadsto \frac{-3}{x} - \color{blue}{\frac{\frac{1}{x}}{x}} \]

   4. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{-3}{x} - \frac{\frac{1}{x}}{x}} \]

   if 5.00000000000000018e-11 < (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

   1. Initial program 99.9%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + 1} + \frac{-1 - x}{x + -1} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\frac{-3}{x} + \frac{\frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{-1 - x}{x + -1}\\ \end{array} \]

Alternative 3: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{-3}{x} + \frac{\frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0)))
   (+ (/ -3.0 x) (/ (/ -1.0 x) x))
   (+ 1.0 (* x 3.0))))

C

double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = (-3.0 / x) + ((-1.0 / x) / x);
	} else {
		tmp = 1.0 + (x * 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = ((-3.0d0) / x) + (((-1.0d0) / x) / x)
    else
        tmp = 1.0d0 + (x * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = (-3.0 / x) + ((-1.0 / x) / x);
	} else {
		tmp = 1.0 + (x * 3.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = (-3.0 / x) + ((-1.0 / x) / x)
	else:
		tmp = 1.0 + (x * 3.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(Float64(-3.0 / x) + Float64(Float64(-1.0 / x) / x));
	else
		tmp = Float64(1.0 + Float64(x * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = (-3.0 / x) + ((-1.0 / x) / x);
	else
		tmp = 1.0 + (x * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(-3.0 / x), $MachinePrecision] + N[(N[(-1.0 / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 9.0%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]

   2. Taylor expanded in x around inf 98.3%

      \[\leadsto \color{blue}{-\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right)} \]
   3. Step-by-step derivation

      1. +-commutative 98.3%

         \[\leadsto -\color{blue}{\left(3 \cdot \frac{1}{x} + \frac{1}{{x}^{2}}\right)} \]

      2. distribute-neg-in 98.3%

         \[\leadsto \color{blue}{\left(-3 \cdot \frac{1}{x}\right) + \left(-\frac{1}{{x}^{2}}\right)} \]

      3. sub-neg 98.3%

         \[\leadsto \color{blue}{\left(-3 \cdot \frac{1}{x}\right) - \frac{1}{{x}^{2}}} \]

      4. associate-*r/ 98.8%

         \[\leadsto \left(-\color{blue}{\frac{3 \cdot 1}{x}}\right) - \frac{1}{{x}^{2}} \]

      5. metadata-eval 98.8%

         \[\leadsto \left(-\frac{\color{blue}{3}}{x}\right) - \frac{1}{{x}^{2}} \]

      6. distribute-neg-frac 98.8%

         \[\leadsto \color{blue}{\frac{-3}{x}} - \frac{1}{{x}^{2}} \]

      7. metadata-eval 98.8%

         \[\leadsto \frac{\color{blue}{-3}}{x} - \frac{1}{{x}^{2}} \]

      8. unpow2 98.8%

         \[\leadsto \frac{-3}{x} - \frac{1}{\color{blue}{x \cdot x}} \]

      9. associate-/r* 98.8%

         \[\leadsto \frac{-3}{x} - \color{blue}{\frac{\frac{1}{x}}{x}} \]

   4. Simplified 98.8%

      \[\leadsto \color{blue}{\frac{-3}{x} - \frac{\frac{1}{x}}{x}} \]

   if -1 < x < 1

   1. Initial program 100.0%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]

   2. Taylor expanded in x around 0 99.1%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{-3}{x} + \frac{\frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot 3\\ \end{array} \]

Alternative 4: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-3}{x} + \frac{\frac{-1}{x}}{x}\\ \mathbf{elif}\;x \leq 0.82:\\ \;\;\;\;1 + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;\frac{-3 + \frac{2}{x}}{x + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.0)
   (+ (/ -3.0 x) (/ (/ -1.0 x) x))
   (if (<= x 0.82) (+ 1.0 (* x 3.0)) (/ (+ -3.0 (/ 2.0 x)) (+ x -1.0)))))

C

double code(double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = (-3.0 / x) + ((-1.0 / x) / x);
	} else if (x <= 0.82) {
		tmp = 1.0 + (x * 3.0);
	} else {
		tmp = (-3.0 + (2.0 / x)) / (x + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = ((-3.0d0) / x) + (((-1.0d0) / x) / x)
    else if (x <= 0.82d0) then
        tmp = 1.0d0 + (x * 3.0d0)
    else
        tmp = ((-3.0d0) + (2.0d0 / x)) / (x + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = (-3.0 / x) + ((-1.0 / x) / x);
	} else if (x <= 0.82) {
		tmp = 1.0 + (x * 3.0);
	} else {
		tmp = (-3.0 + (2.0 / x)) / (x + -1.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.0:
		tmp = (-3.0 / x) + ((-1.0 / x) / x)
	elif x <= 0.82:
		tmp = 1.0 + (x * 3.0)
	else:
		tmp = (-3.0 + (2.0 / x)) / (x + -1.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(-3.0 / x) + Float64(Float64(-1.0 / x) / x));
	elseif (x <= 0.82)
		tmp = Float64(1.0 + Float64(x * 3.0));
	else
		tmp = Float64(Float64(-3.0 + Float64(2.0 / x)) / Float64(x + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = (-3.0 / x) + ((-1.0 / x) / x);
	elseif (x <= 0.82)
		tmp = 1.0 + (x * 3.0);
	else
		tmp = (-3.0 + (2.0 / x)) / (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.0], N[(N[(-3.0 / x), $MachinePrecision] + N[(N[(-1.0 / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.82], N[(1.0 + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(-3.0 + N[(2.0 / x), $MachinePrecision]), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 8.4%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]

   2. Taylor expanded in x around inf 98.4%

      \[\leadsto \color{blue}{-\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right)} \]
   3. Step-by-step derivation

      1. +-commutative 98.4%

         \[\leadsto -\color{blue}{\left(3 \cdot \frac{1}{x} + \frac{1}{{x}^{2}}\right)} \]

      2. distribute-neg-in 98.4%

         \[\leadsto \color{blue}{\left(-3 \cdot \frac{1}{x}\right) + \left(-\frac{1}{{x}^{2}}\right)} \]

      3. sub-neg 98.4%

         \[\leadsto \color{blue}{\left(-3 \cdot \frac{1}{x}\right) - \frac{1}{{x}^{2}}} \]

      4. associate-*r/ 98.9%

         \[\leadsto \left(-\color{blue}{\frac{3 \cdot 1}{x}}\right) - \frac{1}{{x}^{2}} \]

      5. metadata-eval 98.9%

         \[\leadsto \left(-\frac{\color{blue}{3}}{x}\right) - \frac{1}{{x}^{2}} \]

      6. distribute-neg-frac 98.9%

         \[\leadsto \color{blue}{\frac{-3}{x}} - \frac{1}{{x}^{2}} \]

      7. metadata-eval 98.9%

         \[\leadsto \frac{\color{blue}{-3}}{x} - \frac{1}{{x}^{2}} \]

      8. unpow2 98.9%

         \[\leadsto \frac{-3}{x} - \frac{1}{\color{blue}{x \cdot x}} \]

      9. associate-/r* 98.9%

         \[\leadsto \frac{-3}{x} - \color{blue}{\frac{\frac{1}{x}}{x}} \]

   4. Simplified 98.9%

      \[\leadsto \color{blue}{\frac{-3}{x} - \frac{\frac{1}{x}}{x}} \]

   if -1 < x < 0.819999999999999951

   1. Initial program 100.0%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]

   2. Taylor expanded in x around 0 99.1%

      \[\leadsto \color{blue}{3 \cdot x + 1} \]

   if 0.819999999999999951 < x

   1. Initial program 9.4%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
   2. Step-by-step derivation

      1. frac-sub 6.3%

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

      2. associate-/r* 6.3%

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

      3. sub-neg 6.3%

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

      4. distribute-rgt-in 6.2%

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

      5. metadata-eval 6.2%

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

      6. neg-mul-1 6.2%

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

      7. fma-def 6.3%

         \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(x, x, -x\right)} - \left(x + 1\right) \cdot \left(x + 1\right)}{x + 1}}{x - 1} \]

      8. fma-neg 6.2%

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

      9. pow2 6.2%

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

      10. sub-neg 6.2%

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

      11. metadata-eval 6.2%

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

   3. Applied egg-rr 6.2%

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

   4. Taylor expanded in x around inf 98.7%

      \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{x} - 3}}{x + -1} \]
   5. Step-by-step derivation

      1. sub-neg 98.7%

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{x} + \left(-3\right)}}{x + -1} \]

      2. associate-*r/ 98.7%

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{x}} + \left(-3\right)}{x + -1} \]

      3. metadata-eval 98.7%

         \[\leadsto \frac{\frac{\color{blue}{2}}{x} + \left(-3\right)}{x + -1} \]

      4. metadata-eval 98.7%

         \[\leadsto \frac{\frac{2}{x} + \color{blue}{-3}}{x + -1} \]

   6. Simplified 98.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-3}{x} + \frac{\frac{-1}{x}}{x}\\ \mathbf{elif}\;x \leq 0.82:\\ \;\;\;\;1 + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;\frac{-3 + \frac{2}{x}}{x + -1}\\ \end{array} \]

Alternative 5: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{-1 + x \cdot -3}{x + 1}}{x + -1} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ (/ (+ -1.0 (* x -3.0)) (+ x 1.0)) (+ x -1.0)))

C

double code(double x) {
	return ((-1.0 + (x * -3.0)) / (x + 1.0)) / (x + -1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (((-1.0d0) + (x * (-3.0d0))) / (x + 1.0d0)) / (x + (-1.0d0))
end function

Java

public static double code(double x) {
	return ((-1.0 + (x * -3.0)) / (x + 1.0)) / (x + -1.0);
}

Python

def code(x):
	return ((-1.0 + (x * -3.0)) / (x + 1.0)) / (x + -1.0)

Julia

function code(x)
	return Float64(Float64(Float64(-1.0 + Float64(x * -3.0)) / Float64(x + 1.0)) / Float64(x + -1.0))
end

MATLAB

function tmp = code(x)
	tmp = ((-1.0 + (x * -3.0)) / (x + 1.0)) / (x + -1.0);
end

Wolfram

code[x_] := N[(N[(N[(-1.0 + N[(x * -3.0), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 56.6%

   \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
2. Step-by-step derivation

   1. frac-sub 54.9%

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

   2. associate-/r* 54.9%

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

   3. sub-neg 54.9%

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

   4. distribute-rgt-in 54.9%

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

   5. metadata-eval 54.9%

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

   6. neg-mul-1 54.9%

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

   7. fma-def 54.9%

      \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(x, x, -x\right)} - \left(x + 1\right) \cdot \left(x + 1\right)}{x + 1}}{x - 1} \]

   8. fma-neg 54.9%

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

   9. pow2 54.9%

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

   10. sub-neg 54.9%

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

   11. metadata-eval 54.9%

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

3. Applied egg-rr 54.9%

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

4. Taylor expanded in x around 0 99.8%

   \[\leadsto \frac{\frac{\color{blue}{-3 \cdot x - 1}}{x + 1}}{x + -1} \]

5. Final simplification 99.8%

   \[\leadsto \frac{\frac{-1 + x \cdot -3}{x + 1}}{x + -1} \]

Alternative 6: 99.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0)))
   (/ (+ -3.0 (/ -1.0 x)) x)
   (+ 1.0 (* x 3.0))))

C

double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = (-3.0 + (-1.0 / x)) / x;
	} else {
		tmp = 1.0 + (x * 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = ((-3.0d0) + ((-1.0d0) / x)) / x
    else
        tmp = 1.0d0 + (x * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = (-3.0 + (-1.0 / x)) / x;
	} else {
		tmp = 1.0 + (x * 3.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = (-3.0 + (-1.0 / x)) / x
	else:
		tmp = 1.0 + (x * 3.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(Float64(-3.0 + Float64(-1.0 / x)) / x);
	else
		tmp = Float64(1.0 + Float64(x * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = (-3.0 + (-1.0 / x)) / x;
	else
		tmp = 1.0 + (x * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(-3.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(1.0 + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 9.0%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
   2. Step-by-step derivation

      1. clear-num 8.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 1}{x}}} - \frac{x + 1}{x - 1} \]

      2. frac-sub 9.2%

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

      3. *-un-lft-identity 9.2%

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

      4. sub-neg 9.2%

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

      5. metadata-eval 9.2%

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

      6. sub-neg 9.2%

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

      7. metadata-eval 9.2%

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

   3. Applied egg-rr 9.2%

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

   4. Taylor expanded in x around inf 98.3%

      \[\leadsto \color{blue}{-\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. +-commutative 98.3%

         \[\leadsto -\color{blue}{\left(3 \cdot \frac{1}{x} + \frac{1}{{x}^{2}}\right)} \]

      2. unpow2 98.3%

         \[\leadsto -\left(3 \cdot \frac{1}{x} + \frac{1}{\color{blue}{x \cdot x}}\right) \]

      3. associate-/l/ 98.3%

         \[\leadsto -\left(3 \cdot \frac{1}{x} + \color{blue}{\frac{\frac{1}{x}}{x}}\right) \]

      4. distribute-neg-in 98.3%

         \[\leadsto \color{blue}{\left(-3 \cdot \frac{1}{x}\right) + \left(-\frac{\frac{1}{x}}{x}\right)} \]

      5. associate-*r/ 98.8%

         \[\leadsto \left(-\color{blue}{\frac{3 \cdot 1}{x}}\right) + \left(-\frac{\frac{1}{x}}{x}\right) \]

      6. metadata-eval 98.8%

         \[\leadsto \left(-\frac{\color{blue}{3}}{x}\right) + \left(-\frac{\frac{1}{x}}{x}\right) \]

      7. distribute-neg-frac 98.8%

         \[\leadsto \color{blue}{\frac{-3}{x}} + \left(-\frac{\frac{1}{x}}{x}\right) \]

      8. metadata-eval 98.8%

         \[\leadsto \frac{\color{blue}{-3}}{x} + \left(-\frac{\frac{1}{x}}{x}\right) \]

      9. unsub-neg 98.8%

         \[\leadsto \color{blue}{\frac{-3}{x} - \frac{\frac{1}{x}}{x}} \]

      10. div-sub 98.8%

          \[\leadsto \color{blue}{\frac{-3 - \frac{1}{x}}{x}} \]

   6. Simplified 98.8%

      \[\leadsto \color{blue}{\frac{-3 - \frac{1}{x}}{x}} \]

   if -1 < x < 1

   1. Initial program 100.0%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]

   2. Taylor expanded in x around 0 99.1%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot 3\\ \end{array} \]

Alternative 7: 98.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1 + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.0) (/ -3.0 x) (if (<= x 1.0) (+ 1.0 (* x 3.0)) (/ -3.0 x))))

C

double code(double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = -3.0 / x;
	} else if (x <= 1.0) {
		tmp = 1.0 + (x * 3.0);
	} else {
		tmp = -3.0 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = (-3.0d0) / x
    else if (x <= 1.0d0) then
        tmp = 1.0d0 + (x * 3.0d0)
    else
        tmp = (-3.0d0) / x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = -3.0 / x;
	} else if (x <= 1.0) {
		tmp = 1.0 + (x * 3.0);
	} else {
		tmp = -3.0 / x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.0:
		tmp = -3.0 / x
	elif x <= 1.0:
		tmp = 1.0 + (x * 3.0)
	else:
		tmp = -3.0 / x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(-3.0 / x);
	elseif (x <= 1.0)
		tmp = Float64(1.0 + Float64(x * 3.0));
	else
		tmp = Float64(-3.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = -3.0 / x;
	elseif (x <= 1.0)
		tmp = 1.0 + (x * 3.0);
	else
		tmp = -3.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.0], N[(-3.0 / x), $MachinePrecision], If[LessEqual[x, 1.0], N[(1.0 + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(-3.0 / x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 9.0%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]

   2. Taylor expanded in x around inf 97.7%

      \[\leadsto \color{blue}{\frac{-3}{x}} \]

   if -1 < x < 1

   1. Initial program 100.0%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]

   2. Taylor expanded in x around 0 99.1%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1 + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x}\\ \end{array} \]

Alternative 8: 98.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.0) (/ -3.0 x) (if (<= x 1.0) (- x -1.0) (/ -3.0 x))))

C

double code(double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = -3.0 / x;
	} else if (x <= 1.0) {
		tmp = x - -1.0;
	} else {
		tmp = -3.0 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = (-3.0d0) / x
    else if (x <= 1.0d0) then
        tmp = x - (-1.0d0)
    else
        tmp = (-3.0d0) / x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = -3.0 / x;
	} else if (x <= 1.0) {
		tmp = x - -1.0;
	} else {
		tmp = -3.0 / x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.0:
		tmp = -3.0 / x
	elif x <= 1.0:
		tmp = x - -1.0
	else:
		tmp = -3.0 / x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(-3.0 / x);
	elseif (x <= 1.0)
		tmp = Float64(x - -1.0);
	else
		tmp = Float64(-3.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = -3.0 / x;
	elseif (x <= 1.0)
		tmp = x - -1.0;
	else
		tmp = -3.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.0], N[(-3.0 / x), $MachinePrecision], If[LessEqual[x, 1.0], N[(x - -1.0), $MachinePrecision], N[(-3.0 / x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 9.0%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]

   2. Taylor expanded in x around inf 97.7%

      \[\leadsto \color{blue}{\frac{-3}{x}} \]

   if -1 < x < 1

   1. Initial program 100.0%

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]

   2. Taylor expanded in x around 0 99.1%

      \[\leadsto \color{blue}{x} - \frac{x + 1}{x - 1} \]

   3. Taylor expanded in x around 0 98.1%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x}\\ \end{array} \]

Alternative 9: 50.2% accurate, 13.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 1.0)

C

double code(double x) {
	return 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0
end function

Java

public static double code(double x) {
	return 1.0;
}

Python

def code(x):
	return 1.0

Julia

function code(x)
	return 1.0
end

MATLAB

function tmp = code(x)
	tmp = 1.0;
end

Wolfram

code[x_] := 1.0

Derivation

1. Initial program 56.6%

   \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]

2. Taylor expanded in x around 0 53.0%

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

3. Final simplification 53.0%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023207 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))