?

Average Error: 29.2 → 11.8
Time: 48.2s
Precision: binary64
Cost: 94033

?

\[\left(\left(-10 \leq w1p \land w1p \leq 10\right) \land \left(-10 \leq ws \land ws \leq 10\right)\right) \land \left(-1000 \leq x \land x \leq 1000\right)\]
\[\frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{-w1p}{2} + \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} - \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{w1p}{2} - \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} \]
↓
\[\begin{array}{l} t_0 := \frac{\log 99 \cdot x}{w1p}\\ t_1 := -2 \cdot t_0\\ t_2 := e^{t_1}\\ t_3 := {\left(t_2 + 1\right)}^{2}\\ t_4 := \left(\frac{\left(\log 99 + t_1\right) \cdot t_2}{t_3} + -2 \cdot \frac{t_2 \cdot \left(\log 99 \cdot -0.5 - t_0\right)}{t_3}\right) \cdot ws\\ t_5 := \frac{w1p}{1 + ws}\\ \mathbf{if}\;w1p \leq -7.6 \cdot 10^{-172}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;w1p \leq -1.6 \cdot 10^{-200}:\\ \;\;\;\;\frac{1}{1 + e^{-2 \cdot \frac{\log 99 \cdot \left(\left(1 + ws\right) \cdot \left(x + \left(w1p \cdot 0.5 + -0.5 \cdot t_5\right)\right)\right)}{w1p}}} + \frac{-1}{1 + e^{-2 \cdot \frac{\log 99 \cdot \left(\left(1 + ws\right) \cdot \left(w1p \cdot -0.5 + \left(x + 0.5 \cdot t_5\right)\right)\right)}{w1p}}}\\ \mathbf{elif}\;w1p \leq -2.1 \cdot 10^{-234} \lor \neg \left(w1p \leq 2.8 \cdot 10^{-152}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + e^{\frac{\log 99 \cdot -2}{t_5} \cdot \left(x + \left(\frac{w1p}{2} - \frac{t_5}{2}\right)\right)}} + \frac{-1}{1 + e^{\left(\left(1 + ws\right) \cdot \left(\log 99 \cdot \frac{-2}{w1p}\right)\right) \cdot \left(x + \frac{t_5 - w1p}{2}\right)}}\\ \end{array} \]
(FPCore (w1p ws x)
 :precision binary64
 (-
  (/
   1.0
   (+
    1.0
    (exp
     (*
      (/ (* (- 2.0) (log 99.0)) (/ w1p (+ 1.0 ws)))
      (- x (+ (/ (- w1p) 2.0) (/ (/ w1p (+ 1.0 ws)) 2.0)))))))
  (/
   1.0
   (+
    1.0
    (exp
     (*
      (/ (* (- 2.0) (log 99.0)) (/ w1p (+ 1.0 ws)))
      (- x (- (/ w1p 2.0) (/ (/ w1p (+ 1.0 ws)) 2.0)))))))))
↓
(FPCore (w1p ws x)
 :precision binary64
 (let* ((t_0 (/ (* (log 99.0) x) w1p))
        (t_1 (* -2.0 t_0))
        (t_2 (exp t_1))
        (t_3 (pow (+ t_2 1.0) 2.0))
        (t_4
         (*
          (+
           (/ (* (+ (log 99.0) t_1) t_2) t_3)
           (* -2.0 (/ (* t_2 (- (* (log 99.0) -0.5) t_0)) t_3)))
          ws))
        (t_5 (/ w1p (+ 1.0 ws))))
   (if (<= w1p -7.6e-172)
     t_4
     (if (<= w1p -1.6e-200)
       (+
        (/
         1.0
         (+
          1.0
          (exp
           (*
            -2.0
            (/
             (* (log 99.0) (* (+ 1.0 ws) (+ x (+ (* w1p 0.5) (* -0.5 t_5)))))
             w1p)))))
        (/
         -1.0
         (+
          1.0
          (exp
           (*
            -2.0
            (/
             (* (log 99.0) (* (+ 1.0 ws) (+ (* w1p -0.5) (+ x (* 0.5 t_5)))))
             w1p))))))
       (if (or (<= w1p -2.1e-234) (not (<= w1p 2.8e-152)))
         t_4
         (+
          (/
           1.0
           (+
            1.0
            (exp
             (*
              (/ (* (log 99.0) -2.0) t_5)
              (+ x (- (/ w1p 2.0) (/ t_5 2.0)))))))
          (/
           -1.0
           (+
            1.0
            (exp
             (*
              (* (+ 1.0 ws) (* (log 99.0) (/ -2.0 w1p)))
              (+ x (/ (- t_5 w1p) 2.0))))))))))))
double code(double w1p, double ws, double x) {
	return (1.0 / (1.0 + exp((((-2.0 * log(99.0)) / (w1p / (1.0 + ws))) * (x - ((-w1p / 2.0) + ((w1p / (1.0 + ws)) / 2.0))))))) - (1.0 / (1.0 + exp((((-2.0 * log(99.0)) / (w1p / (1.0 + ws))) * (x - ((w1p / 2.0) - ((w1p / (1.0 + ws)) / 2.0)))))));
}
↓
double code(double w1p, double ws, double x) {
	double t_0 = (log(99.0) * x) / w1p;
	double t_1 = -2.0 * t_0;
	double t_2 = exp(t_1);
	double t_3 = pow((t_2 + 1.0), 2.0);
	double t_4 = ((((log(99.0) + t_1) * t_2) / t_3) + (-2.0 * ((t_2 * ((log(99.0) * -0.5) - t_0)) / t_3))) * ws;
	double t_5 = w1p / (1.0 + ws);
	double tmp;
	if (w1p <= -7.6e-172) {
		tmp = t_4;
	} else if (w1p <= -1.6e-200) {
		tmp = (1.0 / (1.0 + exp((-2.0 * ((log(99.0) * ((1.0 + ws) * (x + ((w1p * 0.5) + (-0.5 * t_5))))) / w1p))))) + (-1.0 / (1.0 + exp((-2.0 * ((log(99.0) * ((1.0 + ws) * ((w1p * -0.5) + (x + (0.5 * t_5))))) / w1p)))));
	} else if ((w1p <= -2.1e-234) || !(w1p <= 2.8e-152)) {
		tmp = t_4;
	} else {
		tmp = (1.0 / (1.0 + exp((((log(99.0) * -2.0) / t_5) * (x + ((w1p / 2.0) - (t_5 / 2.0))))))) + (-1.0 / (1.0 + exp((((1.0 + ws) * (log(99.0) * (-2.0 / w1p))) * (x + ((t_5 - w1p) / 2.0))))));
	}
	return tmp;
}

real(8) function code(w1p, ws, x)
    real(8), intent (in) :: w1p
    real(8), intent (in) :: ws
    real(8), intent (in) :: x
    code = (1.0d0 / (1.0d0 + exp((((-2.0d0 * log(99.0d0)) / (w1p / (1.0d0 + ws))) * (x - ((-w1p / 2.0d0) + ((w1p / (1.0d0 + ws)) / 2.0d0))))))) - (1.0d0 / (1.0d0 + exp((((-2.0d0 * log(99.0d0)) / (w1p / (1.0d0 + ws))) * (x - ((w1p / 2.0d0) - ((w1p / (1.0d0 + ws)) / 2.0d0)))))))
end function
↓
real(8) function code(w1p, ws, x)
    real(8), intent (in) :: w1p
    real(8), intent (in) :: ws
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (log(99.0d0) * x) / w1p
    t_1 = (-2.0d0) * t_0
    t_2 = exp(t_1)
    t_3 = (t_2 + 1.0d0) ** 2.0d0
    t_4 = ((((log(99.0d0) + t_1) * t_2) / t_3) + ((-2.0d0) * ((t_2 * ((log(99.0d0) * (-0.5d0)) - t_0)) / t_3))) * ws
    t_5 = w1p / (1.0d0 + ws)
    if (w1p <= (-7.6d-172)) then
        tmp = t_4
    else if (w1p <= (-1.6d-200)) then
        tmp = (1.0d0 / (1.0d0 + exp(((-2.0d0) * ((log(99.0d0) * ((1.0d0 + ws) * (x + ((w1p * 0.5d0) + ((-0.5d0) * t_5))))) / w1p))))) + ((-1.0d0) / (1.0d0 + exp(((-2.0d0) * ((log(99.0d0) * ((1.0d0 + ws) * ((w1p * (-0.5d0)) + (x + (0.5d0 * t_5))))) / w1p)))))
    else if ((w1p <= (-2.1d-234)) .or. (.not. (w1p <= 2.8d-152))) then
        tmp = t_4
    else
        tmp = (1.0d0 / (1.0d0 + exp((((log(99.0d0) * (-2.0d0)) / t_5) * (x + ((w1p / 2.0d0) - (t_5 / 2.0d0))))))) + ((-1.0d0) / (1.0d0 + exp((((1.0d0 + ws) * (log(99.0d0) * ((-2.0d0) / w1p))) * (x + ((t_5 - w1p) / 2.0d0))))))
    end if
    code = tmp
end function

public static double code(double w1p, double ws, double x) {
	return (1.0 / (1.0 + Math.exp((((-2.0 * Math.log(99.0)) / (w1p / (1.0 + ws))) * (x - ((-w1p / 2.0) + ((w1p / (1.0 + ws)) / 2.0))))))) - (1.0 / (1.0 + Math.exp((((-2.0 * Math.log(99.0)) / (w1p / (1.0 + ws))) * (x - ((w1p / 2.0) - ((w1p / (1.0 + ws)) / 2.0)))))));
}
↓
public static double code(double w1p, double ws, double x) {
	double t_0 = (Math.log(99.0) * x) / w1p;
	double t_1 = -2.0 * t_0;
	double t_2 = Math.exp(t_1);
	double t_3 = Math.pow((t_2 + 1.0), 2.0);
	double t_4 = ((((Math.log(99.0) + t_1) * t_2) / t_3) + (-2.0 * ((t_2 * ((Math.log(99.0) * -0.5) - t_0)) / t_3))) * ws;
	double t_5 = w1p / (1.0 + ws);
	double tmp;
	if (w1p <= -7.6e-172) {
		tmp = t_4;
	} else if (w1p <= -1.6e-200) {
		tmp = (1.0 / (1.0 + Math.exp((-2.0 * ((Math.log(99.0) * ((1.0 + ws) * (x + ((w1p * 0.5) + (-0.5 * t_5))))) / w1p))))) + (-1.0 / (1.0 + Math.exp((-2.0 * ((Math.log(99.0) * ((1.0 + ws) * ((w1p * -0.5) + (x + (0.5 * t_5))))) / w1p)))));
	} else if ((w1p <= -2.1e-234) || !(w1p <= 2.8e-152)) {
		tmp = t_4;
	} else {
		tmp = (1.0 / (1.0 + Math.exp((((Math.log(99.0) * -2.0) / t_5) * (x + ((w1p / 2.0) - (t_5 / 2.0))))))) + (-1.0 / (1.0 + Math.exp((((1.0 + ws) * (Math.log(99.0) * (-2.0 / w1p))) * (x + ((t_5 - w1p) / 2.0))))));
	}
	return tmp;
}

def code(w1p, ws, x):
	return (1.0 / (1.0 + math.exp((((-2.0 * math.log(99.0)) / (w1p / (1.0 + ws))) * (x - ((-w1p / 2.0) + ((w1p / (1.0 + ws)) / 2.0))))))) - (1.0 / (1.0 + math.exp((((-2.0 * math.log(99.0)) / (w1p / (1.0 + ws))) * (x - ((w1p / 2.0) - ((w1p / (1.0 + ws)) / 2.0)))))))
↓
def code(w1p, ws, x):
	t_0 = (math.log(99.0) * x) / w1p
	t_1 = -2.0 * t_0
	t_2 = math.exp(t_1)
	t_3 = math.pow((t_2 + 1.0), 2.0)
	t_4 = ((((math.log(99.0) + t_1) * t_2) / t_3) + (-2.0 * ((t_2 * ((math.log(99.0) * -0.5) - t_0)) / t_3))) * ws
	t_5 = w1p / (1.0 + ws)
	tmp = 0
	if w1p <= -7.6e-172:
		tmp = t_4
	elif w1p <= -1.6e-200:
		tmp = (1.0 / (1.0 + math.exp((-2.0 * ((math.log(99.0) * ((1.0 + ws) * (x + ((w1p * 0.5) + (-0.5 * t_5))))) / w1p))))) + (-1.0 / (1.0 + math.exp((-2.0 * ((math.log(99.0) * ((1.0 + ws) * ((w1p * -0.5) + (x + (0.5 * t_5))))) / w1p)))))
	elif (w1p <= -2.1e-234) or not (w1p <= 2.8e-152):
		tmp = t_4
	else:
		tmp = (1.0 / (1.0 + math.exp((((math.log(99.0) * -2.0) / t_5) * (x + ((w1p / 2.0) - (t_5 / 2.0))))))) + (-1.0 / (1.0 + math.exp((((1.0 + ws) * (math.log(99.0) * (-2.0 / w1p))) * (x + ((t_5 - w1p) / 2.0))))))
	return tmp

function code(w1p, ws, x)
	return Float64(Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Float64(Float64(-2.0) * log(99.0)) / Float64(w1p / Float64(1.0 + ws))) * Float64(x - Float64(Float64(Float64(-w1p) / 2.0) + Float64(Float64(w1p / Float64(1.0 + ws)) / 2.0))))))) - Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Float64(Float64(-2.0) * log(99.0)) / Float64(w1p / Float64(1.0 + ws))) * Float64(x - Float64(Float64(w1p / 2.0) - Float64(Float64(w1p / Float64(1.0 + ws)) / 2.0))))))))
end
↓
function code(w1p, ws, x)
	t_0 = Float64(Float64(log(99.0) * x) / w1p)
	t_1 = Float64(-2.0 * t_0)
	t_2 = exp(t_1)
	t_3 = Float64(t_2 + 1.0) ^ 2.0
	t_4 = Float64(Float64(Float64(Float64(Float64(log(99.0) + t_1) * t_2) / t_3) + Float64(-2.0 * Float64(Float64(t_2 * Float64(Float64(log(99.0) * -0.5) - t_0)) / t_3))) * ws)
	t_5 = Float64(w1p / Float64(1.0 + ws))
	tmp = 0.0
	if (w1p <= -7.6e-172)
		tmp = t_4;
	elseif (w1p <= -1.6e-200)
		tmp = Float64(Float64(1.0 / Float64(1.0 + exp(Float64(-2.0 * Float64(Float64(log(99.0) * Float64(Float64(1.0 + ws) * Float64(x + Float64(Float64(w1p * 0.5) + Float64(-0.5 * t_5))))) / w1p))))) + Float64(-1.0 / Float64(1.0 + exp(Float64(-2.0 * Float64(Float64(log(99.0) * Float64(Float64(1.0 + ws) * Float64(Float64(w1p * -0.5) + Float64(x + Float64(0.5 * t_5))))) / w1p))))));
	elseif ((w1p <= -2.1e-234) || !(w1p <= 2.8e-152))
		tmp = t_4;
	else
		tmp = Float64(Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Float64(log(99.0) * -2.0) / t_5) * Float64(x + Float64(Float64(w1p / 2.0) - Float64(t_5 / 2.0))))))) + Float64(-1.0 / Float64(1.0 + exp(Float64(Float64(Float64(1.0 + ws) * Float64(log(99.0) * Float64(-2.0 / w1p))) * Float64(x + Float64(Float64(t_5 - w1p) / 2.0)))))));
	end
	return tmp
end

function tmp = code(w1p, ws, x)
	tmp = (1.0 / (1.0 + exp((((-2.0 * log(99.0)) / (w1p / (1.0 + ws))) * (x - ((-w1p / 2.0) + ((w1p / (1.0 + ws)) / 2.0))))))) - (1.0 / (1.0 + exp((((-2.0 * log(99.0)) / (w1p / (1.0 + ws))) * (x - ((w1p / 2.0) - ((w1p / (1.0 + ws)) / 2.0)))))));
end
↓
function tmp_2 = code(w1p, ws, x)
	t_0 = (log(99.0) * x) / w1p;
	t_1 = -2.0 * t_0;
	t_2 = exp(t_1);
	t_3 = (t_2 + 1.0) ^ 2.0;
	t_4 = ((((log(99.0) + t_1) * t_2) / t_3) + (-2.0 * ((t_2 * ((log(99.0) * -0.5) - t_0)) / t_3))) * ws;
	t_5 = w1p / (1.0 + ws);
	tmp = 0.0;
	if (w1p <= -7.6e-172)
		tmp = t_4;
	elseif (w1p <= -1.6e-200)
		tmp = (1.0 / (1.0 + exp((-2.0 * ((log(99.0) * ((1.0 + ws) * (x + ((w1p * 0.5) + (-0.5 * t_5))))) / w1p))))) + (-1.0 / (1.0 + exp((-2.0 * ((log(99.0) * ((1.0 + ws) * ((w1p * -0.5) + (x + (0.5 * t_5))))) / w1p)))));
	elseif ((w1p <= -2.1e-234) || ~((w1p <= 2.8e-152)))
		tmp = t_4;
	else
		tmp = (1.0 / (1.0 + exp((((log(99.0) * -2.0) / t_5) * (x + ((w1p / 2.0) - (t_5 / 2.0))))))) + (-1.0 / (1.0 + exp((((1.0 + ws) * (log(99.0) * (-2.0 / w1p))) * (x + ((t_5 - w1p) / 2.0))))));
	end
	tmp_2 = tmp;
end

code[w1p_, ws_, x_] := N[(N[(1.0 / N[(1.0 + N[Exp[N[(N[(N[((-2.0) * N[Log[99.0], $MachinePrecision]), $MachinePrecision] / N[(w1p / N[(1.0 + ws), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - N[(N[((-w1p) / 2.0), $MachinePrecision] + N[(N[(w1p / N[(1.0 + ws), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(1.0 / N[(1.0 + N[Exp[N[(N[(N[((-2.0) * N[Log[99.0], $MachinePrecision]), $MachinePrecision] / N[(w1p / N[(1.0 + ws), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - N[(N[(w1p / 2.0), $MachinePrecision] - N[(N[(w1p / N[(1.0 + ws), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[w1p_, ws_, x_] := Block[{t$95$0 = N[(N[(N[Log[99.0], $MachinePrecision] * x), $MachinePrecision] / w1p), $MachinePrecision]}, Block[{t$95$1 = N[(-2.0 * t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[Exp[t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Power[N[(t$95$2 + 1.0), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(N[Log[99.0], $MachinePrecision] + t$95$1), $MachinePrecision] * t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(-2.0 * N[(N[(t$95$2 * N[(N[(N[Log[99.0], $MachinePrecision] * -0.5), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * ws), $MachinePrecision]}, Block[{t$95$5 = N[(w1p / N[(1.0 + ws), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[w1p, -7.6e-172], t$95$4, If[LessEqual[w1p, -1.6e-200], N[(N[(1.0 / N[(1.0 + N[Exp[N[(-2.0 * N[(N[(N[Log[99.0], $MachinePrecision] * N[(N[(1.0 + ws), $MachinePrecision] * N[(x + N[(N[(w1p * 0.5), $MachinePrecision] + N[(-0.5 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / w1p), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / N[(1.0 + N[Exp[N[(-2.0 * N[(N[(N[Log[99.0], $MachinePrecision] * N[(N[(1.0 + ws), $MachinePrecision] * N[(N[(w1p * -0.5), $MachinePrecision] + N[(x + N[(0.5 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / w1p), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[w1p, -2.1e-234], N[Not[LessEqual[w1p, 2.8e-152]], $MachinePrecision]], t$95$4, N[(N[(1.0 / N[(1.0 + N[Exp[N[(N[(N[(N[Log[99.0], $MachinePrecision] * -2.0), $MachinePrecision] / t$95$5), $MachinePrecision] * N[(x + N[(N[(w1p / 2.0), $MachinePrecision] - N[(t$95$5 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / N[(1.0 + N[Exp[N[(N[(N[(1.0 + ws), $MachinePrecision] * N[(N[Log[99.0], $MachinePrecision] * N[(-2.0 / w1p), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x + N[(N[(t$95$5 - w1p), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

\frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{-w1p}{2} + \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} - \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{w1p}{2} - \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}}
↓
\begin{array}{l}
t_0 := \frac{\log 99 \cdot x}{w1p}\\
t_1 := -2 \cdot t_0\\
t_2 := e^{t_1}\\
t_3 := {\left(t_2 + 1\right)}^{2}\\
t_4 := \left(\frac{\left(\log 99 + t_1\right) \cdot t_2}{t_3} + -2 \cdot \frac{t_2 \cdot \left(\log 99 \cdot -0.5 - t_0\right)}{t_3}\right) \cdot ws\\
t_5 := \frac{w1p}{1 + ws}\\
\mathbf{if}\;w1p \leq -7.6 \cdot 10^{-172}:\\
\;\;\;\;t_4\\

\mathbf{elif}\;w1p \leq -1.6 \cdot 10^{-200}:\\
\;\;\;\;\frac{1}{1 + e^{-2 \cdot \frac{\log 99 \cdot \left(\left(1 + ws\right) \cdot \left(x + \left(w1p \cdot 0.5 + -0.5 \cdot t_5\right)\right)\right)}{w1p}}} + \frac{-1}{1 + e^{-2 \cdot \frac{\log 99 \cdot \left(\left(1 + ws\right) \cdot \left(w1p \cdot -0.5 + \left(x + 0.5 \cdot t_5\right)\right)\right)}{w1p}}}\\

\mathbf{elif}\;w1p \leq -2.1 \cdot 10^{-234} \lor \neg \left(w1p \leq 2.8 \cdot 10^{-152}\right):\\
\;\;\;\;t_4\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{1 + e^{\frac{\log 99 \cdot -2}{t_5} \cdot \left(x + \left(\frac{w1p}{2} - \frac{t_5}{2}\right)\right)}} + \frac{-1}{1 + e^{\left(\left(1 + ws\right) \cdot \left(\log 99 \cdot \frac{-2}{w1p}\right)\right) \cdot \left(x + \frac{t_5 - w1p}{2}\right)}}\\


\end{array}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Split input into 3 regimes

  2. if w1p < -7.59999999999999974e-172 or -1.59999999999999991e-200 < w1p < -2.09999999999999991e-234 or 2.79999999999999984e-152 < w1p

    1. Initial program 40.7

      \[\frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{-w1p}{2} + \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} - \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{w1p}{2} - \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} \]

    2. Simplified41.8

      \[\leadsto \color{blue}{\frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \left(\frac{-w1p}{2} + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}}} \]
      Proof

      [Start]40.7

      \[ \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{-w1p}{2} + \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} - \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{w1p}{2} - \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} \]

    3. Applied egg-rr41.9

      \[\leadsto \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \color{blue}{\frac{2 + \left(2 \cdot \frac{1 + ws}{w1p}\right) \cdot \left(-w1p\right)}{\left(2 \cdot \frac{1 + ws}{w1p}\right) \cdot 2}}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

    4. Simplified41.9

      \[\leadsto \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \color{blue}{\frac{2 + \left(w1p \cdot -2\right) \cdot \frac{1 + ws}{w1p}}{\frac{1 + ws}{\frac{w1p}{4}}}}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]
      Proof

      [Start]41.9

      \[ \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \frac{2 + \left(2 \cdot \frac{1 + ws}{w1p}\right) \cdot \left(-w1p\right)}{\left(2 \cdot \frac{1 + ws}{w1p}\right) \cdot 2}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

      *-commutative [<=]41.9

      \[ \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \frac{2 + \color{blue}{\left(-w1p\right) \cdot \left(2 \cdot \frac{1 + ws}{w1p}\right)}}{\left(2 \cdot \frac{1 + ws}{w1p}\right) \cdot 2}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

      associate-*r* [=>]41.9

      \[ \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \frac{2 + \color{blue}{\left(\left(-w1p\right) \cdot 2\right) \cdot \frac{1 + ws}{w1p}}}{\left(2 \cdot \frac{1 + ws}{w1p}\right) \cdot 2}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

      distribute-lft-neg-out [=>]41.9

      \[ \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \frac{2 + \color{blue}{\left(-w1p \cdot 2\right)} \cdot \frac{1 + ws}{w1p}}{\left(2 \cdot \frac{1 + ws}{w1p}\right) \cdot 2}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

      distribute-rgt-neg-in [=>]41.9

      \[ \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \frac{2 + \color{blue}{\left(w1p \cdot \left(-2\right)\right)} \cdot \frac{1 + ws}{w1p}}{\left(2 \cdot \frac{1 + ws}{w1p}\right) \cdot 2}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

      metadata-eval [=>]41.9

      \[ \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \frac{2 + \left(w1p \cdot \color{blue}{-2}\right) \cdot \frac{1 + ws}{w1p}}{\left(2 \cdot \frac{1 + ws}{w1p}\right) \cdot 2}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

      *-commutative [<=]41.9

      \[ \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \frac{2 + \left(w1p \cdot -2\right) \cdot \frac{1 + ws}{w1p}}{\color{blue}{2 \cdot \left(2 \cdot \frac{1 + ws}{w1p}\right)}}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

      associate-*r* [=>]41.9

      \[ \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \frac{2 + \left(w1p \cdot -2\right) \cdot \frac{1 + ws}{w1p}}{\color{blue}{\left(2 \cdot 2\right) \cdot \frac{1 + ws}{w1p}}}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

      metadata-eval [=>]41.9

      \[ \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \frac{2 + \left(w1p \cdot -2\right) \cdot \frac{1 + ws}{w1p}}{\color{blue}{4} \cdot \frac{1 + ws}{w1p}}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

      associate-*r/ [=>]41.9

      \[ \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \frac{2 + \left(w1p \cdot -2\right) \cdot \frac{1 + ws}{w1p}}{\color{blue}{\frac{4 \cdot \left(1 + ws\right)}{w1p}}}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

      *-commutative [=>]41.9

      \[ \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \frac{2 + \left(w1p \cdot -2\right) \cdot \frac{1 + ws}{w1p}}{\frac{\color{blue}{\left(1 + ws\right) \cdot 4}}{w1p}}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

      associate-/l* [=>]41.9

      \[ \frac{1}{1 + e^{\left(\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)\right) \cdot \left(x - \frac{2 + \left(w1p \cdot -2\right) \cdot \frac{1 + ws}{w1p}}{\color{blue}{\frac{1 + ws}{\frac{w1p}{4}}}}\right)}} - \frac{1}{1 + {\left(e^{\frac{-2 \cdot \log 99}{w1p} \cdot \left(1 + ws\right)}\right)}^{\left(\left(x - \frac{w1p}{2}\right) + \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)}} \]

    5. Taylor expanded in ws around 0 10.4

      \[\leadsto \color{blue}{\left(\frac{\left(\log 99 + -2 \cdot \frac{\log 99 \cdot x}{w1p}\right) \cdot e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}}}{{\left(1 + e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}}\right)}^{2}} - -2 \cdot \frac{\left(\frac{\log 99 \cdot x}{w1p} + 0.5 \cdot \log 99\right) \cdot e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}}}{{\left(1 + e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}}\right)}^{2}}\right) \cdot ws} \]

    if -7.59999999999999974e-172 < w1p < -1.59999999999999991e-200

    1. Initial program 24.0

      \[\frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{-w1p}{2} + \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} - \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{w1p}{2} - \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} \]

    2. Taylor expanded in w1p around 0 24.0

      \[\leadsto \color{blue}{\frac{1}{1 + e^{-2 \cdot \frac{\log 99 \cdot \left(\left(x - \left(-0.5 \cdot w1p + 0.5 \cdot \frac{w1p}{1 + ws}\right)\right) \cdot \left(1 + ws\right)\right)}{w1p}}} - \frac{1}{1 + e^{-2 \cdot \frac{\log 99 \cdot \left(\left(1 + ws\right) \cdot \left(\left(0.5 \cdot \frac{w1p}{1 + ws} + x\right) - 0.5 \cdot w1p\right)\right)}{w1p}}}} \]

    if -2.09999999999999991e-234 < w1p < 2.79999999999999984e-152

    1. Initial program 12.3

      \[\frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{-w1p}{2} + \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} - \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{w1p}{2} - \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} \]

    2. Applied egg-rr12.3

      \[\leadsto \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{-w1p}{2} + \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} - \frac{1}{1 + e^{\color{blue}{{\left(\left(\left(1 + ws\right) \cdot \frac{-2 \cdot \log 99}{w1p}\right) \cdot \left(x - \frac{w1p - \frac{w1p}{1 + ws}}{2}\right)\right)}^{1}}}} \]

    3. Simplified12.3

      \[\leadsto \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{-w1p}{2} + \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} - \frac{1}{1 + e^{\color{blue}{\left(\left(1 + ws\right) \cdot \left(\frac{-2}{w1p} \cdot \log 99\right)\right) \cdot \left(x - \frac{w1p - \frac{w1p}{1 + ws}}{2}\right)}}} \]
      Proof

      [Start]12.3

      \[ \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{-w1p}{2} + \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} - \frac{1}{1 + e^{{\left(\left(\left(1 + ws\right) \cdot \frac{-2 \cdot \log 99}{w1p}\right) \cdot \left(x - \frac{w1p - \frac{w1p}{1 + ws}}{2}\right)\right)}^{1}}} \]

      unpow1 [=>]12.3

      \[ \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{-w1p}{2} + \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} - \frac{1}{1 + e^{\color{blue}{\left(\left(1 + ws\right) \cdot \frac{-2 \cdot \log 99}{w1p}\right) \cdot \left(x - \frac{w1p - \frac{w1p}{1 + ws}}{2}\right)}}} \]

      associate-/l* [=>]12.3

      \[ \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{-w1p}{2} + \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} - \frac{1}{1 + e^{\left(\left(1 + ws\right) \cdot \color{blue}{\frac{-2}{\frac{w1p}{\log 99}}}\right) \cdot \left(x - \frac{w1p - \frac{w1p}{1 + ws}}{2}\right)}} \]

      associate-/r/ [=>]12.3

      \[ \frac{1}{1 + e^{\frac{\left(-2\right) \cdot \log 99}{\frac{w1p}{1 + ws}} \cdot \left(x - \left(\frac{-w1p}{2} + \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} - \frac{1}{1 + e^{\left(\left(1 + ws\right) \cdot \color{blue}{\left(\frac{-2}{w1p} \cdot \log 99\right)}\right) \cdot \left(x - \frac{w1p - \frac{w1p}{1 + ws}}{2}\right)}} \]
  3. Recombined 3 regimes into one program.

  4. Final simplification11.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;w1p \leq -7.6 \cdot 10^{-172}:\\ \;\;\;\;\left(\frac{\left(\log 99 + -2 \cdot \frac{\log 99 \cdot x}{w1p}\right) \cdot e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}}}{{\left(e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}} + 1\right)}^{2}} + -2 \cdot \frac{e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}} \cdot \left(\log 99 \cdot -0.5 - \frac{\log 99 \cdot x}{w1p}\right)}{{\left(e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}} + 1\right)}^{2}}\right) \cdot ws\\ \mathbf{elif}\;w1p \leq -1.6 \cdot 10^{-200}:\\ \;\;\;\;\frac{1}{1 + e^{-2 \cdot \frac{\log 99 \cdot \left(\left(1 + ws\right) \cdot \left(x + \left(w1p \cdot 0.5 + -0.5 \cdot \frac{w1p}{1 + ws}\right)\right)\right)}{w1p}}} + \frac{-1}{1 + e^{-2 \cdot \frac{\log 99 \cdot \left(\left(1 + ws\right) \cdot \left(w1p \cdot -0.5 + \left(x + 0.5 \cdot \frac{w1p}{1 + ws}\right)\right)\right)}{w1p}}}\\ \mathbf{elif}\;w1p \leq -2.1 \cdot 10^{-234} \lor \neg \left(w1p \leq 2.8 \cdot 10^{-152}\right):\\ \;\;\;\;\left(\frac{\left(\log 99 + -2 \cdot \frac{\log 99 \cdot x}{w1p}\right) \cdot e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}}}{{\left(e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}} + 1\right)}^{2}} + -2 \cdot \frac{e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}} \cdot \left(\log 99 \cdot -0.5 - \frac{\log 99 \cdot x}{w1p}\right)}{{\left(e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}} + 1\right)}^{2}}\right) \cdot ws\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + e^{\frac{\log 99 \cdot -2}{\frac{w1p}{1 + ws}} \cdot \left(x + \left(\frac{w1p}{2} - \frac{\frac{w1p}{1 + ws}}{2}\right)\right)}} + \frac{-1}{1 + e^{\left(\left(1 + ws\right) \cdot \left(\log 99 \cdot \frac{-2}{w1p}\right)\right) \cdot \left(x + \frac{\frac{w1p}{1 + ws} - w1p}{2}\right)}}\\ \end{array} \]

Alternatives

Alternative 1
Error29.3
Cost29120
\[\begin{array}{l} t_0 := \frac{w1p}{1 + ws}\\ \frac{1}{1 + e^{-2 \cdot \frac{\log 99 \cdot \left(\left(1 + ws\right) \cdot \left(x + \left(w1p \cdot 0.5 + -0.5 \cdot t_0\right)\right)\right)}{w1p}}} + \frac{-1}{1 + e^{-2 \cdot \frac{\log 99 \cdot \left(\left(1 + ws\right) \cdot \left(w1p \cdot -0.5 + \left(x + 0.5 \cdot t_0\right)\right)\right)}{w1p}}} \end{array} \]
Alternative 2
Error29.9
Cost28480
\[\begin{array}{l} t_0 := \frac{w1p}{1 + ws}\\ \frac{1}{1 + e^{\frac{\log 99 \cdot -2}{t_0} \cdot \left(x + w1p \cdot 0\right)}} + \frac{-1}{1 + e^{\left(\left(1 + ws\right) \cdot \left(\log 99 \cdot \frac{-2}{w1p}\right)\right) \cdot \left(x + \frac{t_0 - w1p}{2}\right)}} \end{array} \]
Alternative 3
Error29.9
Cost28096
\[\frac{1}{1 + e^{\left(\left(1 + ws\right) \cdot \frac{\log 99 \cdot -2}{w1p}\right) \cdot \left(x + \left(\frac{w1p}{2} - \frac{w1p}{2 \cdot \left(1 + ws\right)}\right)\right)}} + \frac{-1}{e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}} + 1} \]
Alternative 4
Error30.1
Cost27072
\[\begin{array}{l} t_0 := \frac{1}{e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}} + 1}\\ t_0 - t_0 \end{array} \]
Alternative 5
Error30.9
Cost21504
\[\frac{1}{1 + e^{\left(-1 + -2 \cdot \frac{-0.5}{1 + ws}\right) \cdot \left(\log 99 \cdot \left(1 + ws\right)\right)}} + \frac{-1}{1 + {99}^{\left(\left(1 + ws\right) \cdot \left(1 + \frac{-1}{1 + ws}\right)\right)}} \]
Alternative 6
Error61.3
Cost13632
\[0.5 + \frac{-1}{e^{-2 \cdot \frac{\log 99 \cdot x}{w1p}} + 1} \]

Error

Reproduce?

herbie shell --seed 1 
(FPCore (w1p ws x)
  :name "1/(1 + exp(-2*log(99.0)/( w1p/(1+ws))*(x-(-w1p/2.0 +  w1p/(1+ws)/2)))) - 1/(1 + exp(-2*log(99.0)/( w1p/(1+ws))*(x-(w1p/2.0 -  w1p/(1+ws)/2))))"
  :precision binary64
  :pre (and (and (and (<= -10.0 w1p) (<= w1p 10.0)) (and (<= -10.0 ws) (<= ws 10.0))) (and (<= -1000.0 x) (<= x 1000.0)))
  (- (/ 1.0 (+ 1.0 (exp (* (/ (* (- 2.0) (log 99.0)) (/ w1p (+ 1.0 ws))) (- x (+ (/ (- w1p) 2.0) (/ (/ w1p (+ 1.0 ws)) 2.0))))))) (/ 1.0 (+ 1.0 (exp (* (/ (* (- 2.0) (log 99.0)) (/ w1p (+ 1.0 ws))) (- x (- (/ w1p 2.0) (/ (/ w1p (+ 1.0 ws)) 2.0)))))))))