diff --git a/pkgs/racket-test-core/tests/racket/math.rktl b/pkgs/racket-test-core/tests/racket/math.rktl
index 99679c5c1b..264e7de9da 100644
--- a/pkgs/racket-test-core/tests/racket/math.rktl
+++ b/pkgs/racket-test-core/tests/racket/math.rktl
@@ -340,7 +340,11 @@
   (test 0.0f0 tanh 0.0f0)
   (test #t single=? tanh+1 (tanh 1.0f0))
   (test 1.0f0 tanh 20.0f0)
-  (test 1.0f0 tanh +inf.f))
+  (test 1.0f0 tanh +inf.f)
+  (test #t single-flonum? (tanh -0.11100646f0))
+  (test #t single-flonum? (tanh 0.11100646f0))
+  (test #t single-flonum? (tanh 0.61100646f0))
+  (test #t single-flonum? (tanh 20.61100646f0)))
 
 (test +nan.0 tanh +nan.0)
 (test -1.0 tanh -inf.0)
diff --git a/racket/collects/racket/math.rkt b/racket/collects/racket/math.rkt
index c2c03b0faf..2f470151ad 100644
--- a/racket/collects/racket/math.rkt
+++ b/racket/collects/racket/math.rkt
@@ -85,7 +85,7 @@
                     (define R
                       (/ (* g (+ (* (+ (* p2 g) p1) g) p0))
                          (+ (* (+ (* (+ g q2) g) q1) g) q0)))
-                    (+ z (* z R))]
+                    (+ z (* z (if (single-flonum? z) (real->single-flonum R) R)))]
                    [(z . < . 19.06154746539849600897D+00) (- 1 (/ 2 (+ 1 (exp (* 2 z)))))]
                    [(z . >= . 19.06154746539849600897D+00) (if (single-flonum? z) (real->single-flonum 1.0) 1.0)]
                    [else          z]))]  ; +nan.0 or +nan.f