Logistic function from Lakshay Garg

Percentage Accurate: 55.4% → 99.3%

Time: 7.9s

Alternatives: 5

Speedup: 18.1×

Specification

Math

\[\begin{array}{l} \\ \frac{2}{1 + e^{-2 \cdot x}} - 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))

C

double code(double x, double y) {
	return (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 / (1.0d0 + exp(((-2.0d0) * x)))) - 1.0d0
end function

Java

public static double code(double x, double y) {
	return (2.0 / (1.0 + Math.exp((-2.0 * x)))) - 1.0;
}

Python

def code(x, y):
	return (2.0 / (1.0 + math.exp((-2.0 * x)))) - 1.0

Julia

function code(x, y)
	return Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) - 1.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
end

Wolfram

code[x_, y_] := N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]

Initial Program: 55.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2}{1 + e^{-2 \cdot x}} - 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))

C

double code(double x, double y) {
	return (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 / (1.0d0 + exp(((-2.0d0) * x)))) - 1.0d0
end function

Java

public static double code(double x, double y) {
	return (2.0 / (1.0 + Math.exp((-2.0 * x)))) - 1.0;
}

Python

def code(x, y):
	return (2.0 / (1.0 + math.exp((-2.0 * x)))) - 1.0

Julia

function code(x, y)
	return Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) - 1.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
end

Wolfram

code[x_, y_] := N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]

Alternative 1: 99.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -400:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} + -1\\ \mathbf{elif}\;-2 \cdot x \leq 2 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + {e}^{\left(-2 \cdot x\right)}} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* -2.0 x) -400.0)
   (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) -1.0)
   (if (<= (* -2.0 x) 2e-11) x (+ (/ 2.0 (+ 1.0 (pow E (* -2.0 x)))) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((-2.0 * x) <= -400.0) {
		tmp = (2.0 / (1.0 + exp((-2.0 * x)))) + -1.0;
	} else if ((-2.0 * x) <= 2e-11) {
		tmp = x;
	} else {
		tmp = (2.0 / (1.0 + pow(((double) M_E), (-2.0 * x)))) + -1.0;
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if ((-2.0 * x) <= -400.0) {
		tmp = (2.0 / (1.0 + Math.exp((-2.0 * x)))) + -1.0;
	} else if ((-2.0 * x) <= 2e-11) {
		tmp = x;
	} else {
		tmp = (2.0 / (1.0 + Math.pow(Math.E, (-2.0 * x)))) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (-2.0 * x) <= -400.0:
		tmp = (2.0 / (1.0 + math.exp((-2.0 * x)))) + -1.0
	elif (-2.0 * x) <= 2e-11:
		tmp = x
	else:
		tmp = (2.0 / (1.0 + math.pow(math.e, (-2.0 * x)))) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(-2.0 * x) <= -400.0)
		tmp = Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) + -1.0);
	elseif (Float64(-2.0 * x) <= 2e-11)
		tmp = x;
	else
		tmp = Float64(Float64(2.0 / Float64(1.0 + (exp(1) ^ Float64(-2.0 * x)))) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((-2.0 * x) <= -400.0)
		tmp = (2.0 / (1.0 + exp((-2.0 * x)))) + -1.0;
	elseif ((-2.0 * x) <= 2e-11)
		tmp = x;
	else
		tmp = (2.0 / (1.0 + (2.71828182845904523536 ^ (-2.0 * x)))) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(-2.0 * x), $MachinePrecision], -400.0], N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[N[(-2.0 * x), $MachinePrecision], 2e-11], x, N[(N[(2.0 / N[(1.0 + N[Power[E, N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal -2 binary64) x) < -400

   1. Initial program 100.0%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   if -400 < (*.f64 #s(literal -2 binary64) x) < 1.99999999999999988e-11

   1. Initial program 6.7%

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

      1. sub-neg 6.7%

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

      2. exp-prod 6.7%

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

      3. metadata-eval 6.7%

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

   3. Simplified 6.7%

      \[\leadsto \color{blue}{\frac{2}{1 + {\left(e^{-2}\right)}^{x}} + -1} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 100.0%

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

   if 1.99999999999999988e-11 < (*.f64 #s(literal -2 binary64) x)

   1. Initial program 100.0%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-un-lft-identity 100.0%

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

      2. exp-prod 100.0%

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

      3. *-commutative 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. exp-1-e 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -400:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} + -1\\ \mathbf{elif}\;-2 \cdot x \leq 2 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + {e}^{\left(-2 \cdot x\right)}} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -400 \lor \neg \left(-2 \cdot x \leq 2 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} + -1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (* -2.0 x) -400.0) (not (<= (* -2.0 x) 2e-11)))
   (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) -1.0)
   x))

C

double code(double x, double y) {
	double tmp;
	if (((-2.0 * x) <= -400.0) || !((-2.0 * x) <= 2e-11)) {
		tmp = (2.0 / (1.0 + exp((-2.0 * x)))) + -1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((((-2.0d0) * x) <= (-400.0d0)) .or. (.not. (((-2.0d0) * x) <= 2d-11))) then
        tmp = (2.0d0 / (1.0d0 + exp(((-2.0d0) * x)))) + (-1.0d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((-2.0 * x) <= -400.0) || !((-2.0 * x) <= 2e-11)) {
		tmp = (2.0 / (1.0 + Math.exp((-2.0 * x)))) + -1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((-2.0 * x) <= -400.0) or not ((-2.0 * x) <= 2e-11):
		tmp = (2.0 / (1.0 + math.exp((-2.0 * x)))) + -1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(-2.0 * x) <= -400.0) || !(Float64(-2.0 * x) <= 2e-11))
		tmp = Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) + -1.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((-2.0 * x) <= -400.0) || ~(((-2.0 * x) <= 2e-11)))
		tmp = (2.0 / (1.0 + exp((-2.0 * x)))) + -1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(-2.0 * x), $MachinePrecision], -400.0], N[Not[LessEqual[N[(-2.0 * x), $MachinePrecision], 2e-11]], $MachinePrecision]], N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal -2 binary64) x) < -400 or 1.99999999999999988e-11 < (*.f64 #s(literal -2 binary64) x)

   1. Initial program 100.0%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   if -400 < (*.f64 #s(literal -2 binary64) x) < 1.99999999999999988e-11

   1. Initial program 6.7%

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

      1. sub-neg 6.7%

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

      2. exp-prod 6.7%

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

      3. metadata-eval 6.7%

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

   3. Simplified 6.7%

      \[\leadsto \color{blue}{\frac{2}{1 + {\left(e^{-2}\right)}^{x}} + -1} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -400 \lor \neg \left(-2 \cdot x \leq 2 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} + -1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{2}{2 + x \cdot \left(x \cdot \left(2 + x \cdot -1.3333333333333333\right) - 2\right)} + -1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.3e-6)
   (+
    (/ 2.0 (+ 2.0 (* x (- (* x (+ 2.0 (* x -1.3333333333333333))) 2.0))))
    -1.0)
   x))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.3e-6) {
		tmp = (2.0 / (2.0 + (x * ((x * (2.0 + (x * -1.3333333333333333))) - 2.0)))) + -1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.3d-6)) then
        tmp = (2.0d0 / (2.0d0 + (x * ((x * (2.0d0 + (x * (-1.3333333333333333d0)))) - 2.0d0)))) + (-1.0d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.3e-6) {
		tmp = (2.0 / (2.0 + (x * ((x * (2.0 + (x * -1.3333333333333333))) - 2.0)))) + -1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.3e-6:
		tmp = (2.0 / (2.0 + (x * ((x * (2.0 + (x * -1.3333333333333333))) - 2.0)))) + -1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.3e-6)
		tmp = Float64(Float64(2.0 / Float64(2.0 + Float64(x * Float64(Float64(x * Float64(2.0 + Float64(x * -1.3333333333333333))) - 2.0)))) + -1.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.3e-6)
		tmp = (2.0 / (2.0 + (x * ((x * (2.0 + (x * -1.3333333333333333))) - 2.0)))) + -1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.3e-6], N[(N[(2.0 / N[(2.0 + N[(x * N[(N[(x * N[(2.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < -6.29999999999999982e-6

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. exp-prod 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{2}{1 + {\left(e^{-2}\right)}^{x}} + -1} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 98.8%

      \[\leadsto \frac{2}{\color{blue}{2 + x \cdot \left(x \cdot \left(2 + -1.3333333333333333 \cdot x\right) - 2\right)}} + -1 \]

   if -6.29999999999999982e-6 < x

   1. Initial program 41.5%

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

      1. sub-neg 41.5%

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

      2. exp-prod 41.5%

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

      3. metadata-eval 41.5%

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

   3. Simplified 41.5%

      \[\leadsto \color{blue}{\frac{2}{1 + {\left(e^{-2}\right)}^{x}} + -1} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 64.8%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{2}{2 + x \cdot \left(x \cdot \left(2 + x \cdot -1.3333333333333333\right) - 2\right)} + -1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.9% accurate, 18.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = -1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = -1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = -1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], -1.0, x]

Derivation

1. Split input into 2 regimes

2. if x < -1

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. exp-prod 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{2}{1 + {\left(e^{-2}\right)}^{x}} + -1} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 98.3%

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

      1. *-commutative 98.3%

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

   7. Simplified 98.3%

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

   8. Taylor expanded in x around inf 100.0%

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

   if -1 < x

   1. Initial program 41.8%

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

      1. sub-neg 41.8%

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

      2. exp-prod 41.8%

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

      3. metadata-eval 41.8%

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

   3. Simplified 41.8%

      \[\leadsto \color{blue}{\frac{2}{1 + {\left(e^{-2}\right)}^{x}} + -1} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 64.6%

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

Alternative 5: 27.5% accurate, 109.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

double code(double x, double y) {
	return -1.0;
}

Fortran

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

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

function tmp = code(x, y)
	tmp = -1.0;
end

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 55.9%

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

   1. sub-neg 55.9%

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

   2. exp-prod 55.9%

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

   3. metadata-eval 55.9%

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

3. Simplified 55.9%

   \[\leadsto \color{blue}{\frac{2}{1 + {\left(e^{-2}\right)}^{x}} + -1} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 27.5%

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

   1. *-commutative 27.5%

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

7. Simplified 27.5%

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

8. Taylor expanded in x around inf 26.5%

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

Reproduce

herbie shell --seed 2024119 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  :precision binary64
  (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))