diff --git a/collects/plot/common/format.rkt b/collects/plot/common/format.rkt
index 8cb4c1b826..a507cb9cf5 100644
--- a/collects/plot/common/format.rkt
+++ b/collects/plot/common/format.rkt
@@ -83,6 +83,9 @@
 (defproc (real->plot-label [x real?] [digits exact-integer?] [scientific? boolean? #t]) any
   (cond
     [(zero? x)  "0"]
+    [(eqv? x +nan.0)  "+nan.0"]
+    [(eqv? x +inf.0)  "+inf.0"]
+    [(eqv? x -inf.0)  "-inf.0"]
     [else
      (define front-sign (if (x . < . 0) "-" ""))
      (define mid-sign (if (x . < . 0) "-" "+"))
@@ -133,6 +136,26 @@
                 [frac-zero?  (format "~a~a" front-sign int-str)]
                 [else        (format "~a~a.~a" front-sign int-str frac-str)])]))]))
 
+(define (format-special x)
+  (case x
+    [(#f)  "#f"]
+    [(+nan.0)  "+nan.0"]
+    [(+inf.0)  "+inf.0"]
+    [(-inf.0)  "-inf.0"]
+    [else  "<unknown>"]))
+
+(defproc (ivl->string [i ivl?] [extra-digits exact-integer? 3]) string?
+  (match-define (ivl a b) i)
+  (cond [(and (not (regular-real? a)) (not (regular-real? b)))
+         (format "[~a,~a]" (format-special a) (format-special b))]
+        [(not (regular-real? a))  (format "[~a,~a]" (format-special a) (real->plot-label b 15))]
+        [(not (regular-real? b))  (format "[~a,~a]" (real->plot-label a 15) (format-special b))]
+        [else
+         (define digits (digits-for-range a b extra-digits))
+         (format "[~a,~a]"
+                 (real->plot-label a digits)
+                 (real->plot-label b digits))]))
+
 (defproc (->plot-label [a any/c] [digits exact-integer? 7]) string?
   (let loop ([a a])
     (cond [(string? a)   a]
diff --git a/collects/plot/contracted/format.rkt b/collects/plot/contracted/format.rkt
index d43e5bb206..d637f44b42 100644
--- a/collects/plot/contracted/format.rkt
+++ b/collects/plot/contracted/format.rkt
@@ -7,5 +7,5 @@
           integer->superscript
           digits-for-range
           real->decimal-string* real->string/trunc
-          real->plot-label ->plot-label
+          real->plot-label ivl->string ->plot-label
           parse-format-string apply-formatter))
diff --git a/collects/plot/plot2d/plot.rkt b/collects/plot/plot2d/plot.rkt
index c7bf219e8b..9e43afda9e 100644
--- a/collects/plot/plot2d/plot.rkt
+++ b/collects/plot/plot2d/plot.rkt
@@ -14,6 +14,7 @@
          "../common/file-type.rkt"
          "../common/deprecation-warning.rkt"
          "../common/contract-doc.rkt"
+         "../common/format.rkt"
          "plot-area.rkt")
 
 ;; Require lazily: without this, Racket complains while generating documentation:
@@ -37,9 +38,9 @@
   (define plot-bounds-rect (bounds-fixpoint renderer-list given-bounds-rect))
   (when (or (not (rect-regular? plot-bounds-rect))
             (rect-zero-area? plot-bounds-rect))
-    (match-define (vector (ivl x-min x-max) (ivl y-min y-max)) plot-bounds-rect)
-    (error 'plot "could not determine sensible plot bounds; got x ∈ [~a,~a], y ∈ [~a,~a]"
-           x-min x-max y-min y-max))
+    (match-define (vector x-ivl y-ivl) plot-bounds-rect)
+    (error 'plot "could not determine sensible plot bounds; got x ∈ ~a, y ∈ ~a"
+           (ivl->string x-ivl) (ivl->string y-ivl)))
   plot-bounds-rect)
 
 (define (get-ticks renderer-list bounds-rect)
diff --git a/collects/plot/plot3d/plot.rkt b/collects/plot/plot3d/plot.rkt
index 3e660596a0..e40b7021a1 100644
--- a/collects/plot/plot3d/plot.rkt
+++ b/collects/plot/plot3d/plot.rkt
@@ -14,6 +14,7 @@
          "../common/file-type.rkt"
          "../common/deprecation-warning.rkt"
          "../common/contract-doc.rkt"
+         "../common/format.rkt"
          "plot-area.rkt")
 
 ;; Require lazily: without this, Racket complains while generating documentation:
@@ -38,9 +39,9 @@
   (define plot-bounds-rect (bounds-fixpoint renderer-list given-bounds-rect))
   (when (or (not (rect-regular? plot-bounds-rect))
             (rect-zero-area? plot-bounds-rect))
-    (match-define (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max)) plot-bounds-rect)
-    (error 'plot "could not determine sensible plot bounds; got x ∈ [~a,~a], y ∈ [~a,~a], z ∈ [~a,~a]"
-           x-min x-max y-min y-max z-min z-max))
+    (match-define (vector x-ivl y-ivl z-ivl) plot-bounds-rect)
+    (error 'plot "could not determine sensible plot bounds; got x ∈ ~a, y ∈ ~a, z ∈ ~a"
+           (ivl->string x-ivl) (ivl->string y-ivl) (ivl->string z-ivl)))
   plot-bounds-rect)
 
 (define (get-ticks renderer-list bounds-rect)