diff --git a/errors.go b/errors.go
index c09971b..fda377a 100644
--- a/errors.go
+++ b/errors.go
@@ -4,21 +4,13 @@
 
 package optimize
 
-import "errors"
+import (
+	"errors"
+	"fmt"
+	"math"
+)
 
 var (
-	// ErrInf signifies the initial function value is infinite.
-	ErrInf = errors.New("optimize: initial function value is infinite")
-
-	// ErrNaN signifies the initial function value is NaN.
-	ErrNaN = errors.New("optimize: initial function value is NaN")
-
-	// ErrGradInf signifies that a component of the initial gradient is infinite.
-	ErrGradInf = errors.New("optimize: initial gradient is infinite")
-
-	// ErrGradNaN signifies that a component of the initial gradient is NaN.
-	ErrGradNaN = errors.New("optimize: initial gradient is NaN")
-
 	// ErrZeroDimensional signifies an optimization was called with an input of length 0.
 	ErrZeroDimensional = errors.New("optimize: zero dimensional input")
 
@@ -36,3 +28,36 @@ var (
 	// due to floating-point arithmetic.
 	ErrNoProgress = errors.New("linesearch: no change in location after Linesearcher step")
 )
+
+// ErrFunc is returned when an initial function value is invalid. The error
+// state may be either +Inf or NaN. ErrFunc satisfies the error interface.
+type ErrFunc float64
+
+func (err ErrFunc) Error() string {
+	switch {
+	case math.IsInf(float64(err), 1):
+		return "optimize: initial function value is infinite"
+	case math.IsNaN(float64(err)):
+		return "optimize: initial function value is NaN"
+	default:
+		panic("optimize: bad ErrFunc")
+	}
+}
+
+// ErrGrad is returned when an initial gradient is invalid. The error gradient
+// may be either ±Inf or NaN. ErrGrad satisfies the error interface.
+type ErrGrad struct {
+	Grad  float64 // Grad is the invalid gradient value.
+	Index int     // Index is the position at which the invalid gradient was found.
+}
+
+func (err ErrGrad) Error() string {
+	switch {
+	case math.IsInf(err.Grad, 0):
+		return fmt.Sprintf("optimize: initial gradient is infinite at position %d", err.Index)
+	case math.IsNaN(err.Grad):
+		return fmt.Sprintf("optimize: initial gradient is NaN at position %d", err.Index)
+	default:
+		panic("optimize: bad ErrGrad")
+	}
+}
diff --git a/local.go b/local.go
index 962f2ee..540c2be 100644
--- a/local.go
+++ b/local.go
@@ -290,18 +290,12 @@ func getStartingLocation(p *Problem, method Method, initX []float64, stats *Stat
 		evaluate(p, loc, eval, stats)
 	}
 
-	if math.IsNaN(loc.F) {
-		return loc, ErrNaN
+	if math.IsInf(loc.F, 1) || math.IsNaN(loc.F) {
+		return loc, ErrFunc(loc.F)
 	}
-	if math.IsInf(loc.F, 1) {
-		return loc, ErrInf
-	}
-	for _, v := range loc.Gradient {
-		if math.IsInf(v, 0) {
-			return loc, ErrGradInf
-		}
-		if math.IsNaN(v) {
-			return loc, ErrGradNaN
+	for i, v := range loc.Gradient {
+		if math.IsInf(v, 0) || math.IsNaN(v) {
+			return loc, ErrGrad{Grad: v, Index: i}
 		}
 	}