Logistic function from Lakshay Garg

Average Error: 29.3 → 0.4

Time: 21.7s

Precision: binary64

Cost: 7496

Math

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

↓

\[\begin{array}{l} t_0 := \frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{if}\;-2 \cdot x \leq -5000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;-2 \cdot x \leq 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
   (if (<= (* -2.0 x) -5000.0) t_0 (if (<= (* -2.0 x) 1e-10) x t_0))))

C

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

↓

double code(double x, double y) {
	double t_0 = (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
	double tmp;
	if ((-2.0 * x) <= -5000.0) {
		tmp = t_0;
	} else if ((-2.0 * x) <= 1e-10) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

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

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (2.0d0 / (1.0d0 + exp(((-2.0d0) * x)))) - 1.0d0
    if (((-2.0d0) * x) <= (-5000.0d0)) then
        tmp = t_0
    else if (((-2.0d0) * x) <= 1d-10) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y) {
	double t_0 = (2.0 / (1.0 + Math.exp((-2.0 * x)))) - 1.0;
	double tmp;
	if ((-2.0 * x) <= -5000.0) {
		tmp = t_0;
	} else if ((-2.0 * x) <= 1e-10) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

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

↓

def code(x, y):
	t_0 = (2.0 / (1.0 + math.exp((-2.0 * x)))) - 1.0
	tmp = 0
	if (-2.0 * x) <= -5000.0:
		tmp = t_0
	elif (-2.0 * x) <= 1e-10:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

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

↓

function code(x, y)
	t_0 = Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) - 1.0)
	tmp = 0.0
	if (Float64(-2.0 * x) <= -5000.0)
		tmp = t_0;
	elseif (Float64(-2.0 * x) <= 1e-10)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y)
	t_0 = (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
	tmp = 0.0;
	if ((-2.0 * x) <= -5000.0)
		tmp = t_0;
	elseif ((-2.0 * x) <= 1e-10)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
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]

↓

code[x_, y_] := Block[{t$95$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], -5000.0], t$95$0, If[LessEqual[N[(-2.0 * x), $MachinePrecision], 1e-10], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 -2 x) < -5e3 or 1.00000000000000004e-10 < (*.f64 -2 x)

   1. Initial program 0.2

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

   if -5e3 < (*.f64 -2 x) < 1.00000000000000004e-10

   1. Initial program 59.0

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

   2. Taylor expanded in x around 0 0.7

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

Alternatives

Alternative 1
Error	30.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  :precision binary64
  (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))