// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Log-Cosh Loss", "LogCosh", overlay=false)

//@function Computes log(cosh(x)) in a numerically stable way
//@doc     For large |x|, cosh(x) ≈ exp(|x|)/2, so log(cosh(x)) ≈ |x| - log(2)
//@param   x The input value
//@returns log(cosh(x))
stable_logcosh(float x) =>
    float LOG2 = 0.6931471805599453
    float absX = math.abs(x)
    // For large values, use asymptotic approximation to avoid overflow
    absX > 20.0 ? absX - LOG2 : math.log(math.cosh(x))

//@function Calculates Log-Cosh Loss
//@doc     Smooth approximation to absolute error, twice differentiable everywhere.
//@doc     Approximates L1 loss for large errors, L2 for small errors.
//@doc     Less sensitive to outliers than MSE.
//@param   actual Series of actual values
//@param   predicted Series of predicted/forecast values
//@param   length Rolling window for averaging
//@returns Mean log-cosh loss over the window
logcosh_loss(series float actual, series float predicted, simple int length) =>
    // Compute log-cosh loss for current bar
    float error = nz(actual, 0.0) - nz(predicted, 0.0)
    float loss = stable_logcosh(error)

    // Rolling mean of losses
    float result = ta.sma(loss, length)
    result

// ---------- Main loop ----------

// Inputs
i_length = input.int(14, "Length", minval=1)
i_actual = input.source(close, "Actual")
i_predicted = input.source(open, "Predicted")

// Calculation
logcosh_value = logcosh_loss(i_actual, i_predicted, i_length)

// Plot
plot(logcosh_value, "Log-Cosh Loss", color=color.yellow, linewidth=2)
hline(0, "Zero", color=color.gray, linestyle=hline.style_dotted)