diff --git a/lib/msun/src/s_cbrtf.c b/lib/msun/src/s_cbrtf.c
index 89398af37c6e..350694351c55 100644
--- a/lib/msun/src/s_cbrtf.c
+++ b/lib/msun/src/s_cbrtf.c
@@ -28,16 +28,11 @@ static const unsigned
 	B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
 	B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
 
-/* |1/cbrt(x) - p(x)| < 2**-14.5 (~[-4.37e-4, 4.366e-5]). */
-static const float
-P0 =  1.5586718321,			/*  0x3fc7828f */
-P1 = -0.78271341324,			/* -0xbf485fe8 */
-P2 =  0.22403796017;			/*  0x3e656a35 */
-
 float
 cbrtf(float x)
 {
-	float r,s,t,w;
+	double r,T;
+	float t;
 	int32_t hx;
 	u_int32_t sign;
 	u_int32_t high;
@@ -58,27 +53,17 @@ cbrtf(float x)
 	} else
 	    SET_FLOAT_WORD(t,sign|(hx/3+B1));
 
-    /* new cbrt to 14 bits */
-	r=(t*t)*(t/x);
-	t=t*((P0+r*P1)+(r*r)*P2);
+    /* first step Newton iteration (solving t*t-x/t == 0) to 16 bits */
+    /* in double precision to avoid problems with denormals */
+	T=t;
+	r=T*T*T;
+	T=T*(x+x+r)/(x+r+r);
 
-    /*
-     * Round t away from zero to 12 bits (sloppily except for ensuring that
-     * the result is larger in magnitude than cbrt(x) but not much more than
-     * 1 12-bit ulp larger).  With rounding towards zero, the error bound
-     * would be ~5/6 instead of ~4/6, and with t 2 12-bit ulps larger the
-     * infinite-precision error in the Newton approximation would affect
-     * the second digit instead of the third digit of 4/6 = 0.666..., etc.
-     */
-	GET_FLOAT_WORD(high,t);
-	SET_FLOAT_WORD(t,(high+0x1800)&0xfffff000);
+    /* second step Newton iteration to 47 bits */
+    /* in double precision for accuracy */
+	r=T*T*T;
+	T=T*(x+x+r)/(x+r+r);
 
-    /* one step Newton iteration to 24 bits with error < 0.669 ulps */
-	s=t*t;				/* t*t is exact */
-	r=x/s;				/* error <= 0.5 ulps; |r| < |t| */
-	w=t+t;				/* t+t is exact */
-	r=(r-t)/(w+r);			/* r-t is exact; w+r ~= 3*t */
-	t=t+t*r;			/* error <= 0.5 + 0.5/3 + epsilon */
-
-	return(t);
+    /* rounding to 24 bits is perfect in round-to-nearest mode */
+	return(T);
 }