diff --git a/docs/notebooks/tutorials/analytical-ir.ipynb b/docs/notebooks/tutorials/analytical-ir.ipynb
index be22977..f92f4e5 100644
--- a/docs/notebooks/tutorials/analytical-ir.ipynb
+++ b/docs/notebooks/tutorials/analytical-ir.ipynb
@@ -187,7 +187,7 @@
    "metadata": {},
    "source": [
     "```{note}\n",
-    "The [core.solve](nuance.core.solve) function returns a function that computes the depth of a transt given its epoch and duration, it has the signature `function(epoch, duration, period=None, depth=None) -> (log_likelihood, weights, variance)`. When the `depth` parameter is set, the function computes the depth of a transit **injected** with this `depth`. Usually `depth=None`, as this feature is only useful for injection-recovery estimates.\n",
+    "The [core.solve](nuance.core.solve) function returns a function that computes the depth of a transt given its epoch and duration, it has the signature `function(epoch, duration, period=None, depth=None) -> (depth, depth_variance, log_likelihood)`. When the `depth` parameter is set, the function computes the depth of a transit **injected** with this `depth`. Usually `depth=None`, as this feature is only useful for injection-recovery estimates.\n",
     "```"
    ]
   },
diff --git a/nuance/core.py b/nuance/core.py
index 1485a3a..c43e0bc 100644
--- a/nuance/core.py
+++ b/nuance/core.py
@@ -115,7 +115,7 @@ def solve(time, flux, gp=None, X=None, model=None):
     callable
         function that computes the log likelihood of data assuming it is drawn from a
         Gaussian Process with a mean linear model. Signature is:
-        :code:`function(epoch, duration, period=None) -> (log_likelihood, weights, variance)`
+        ``function(epoch, duration, period=None) -> (depth, depth_variance, log_likelihood)``
     """
 
     X, gp, model = check_default(time, X, gp, model)