diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index d9e6d037d..b50ceb9d2 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -1097,62 +1097,68 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet patan_double(const Pa
 }
 
 /** \internal \returns the hyperbolic tan of \a a (coeff-wise)
-    Doesn't do anything fancy, just a 13/6-degree rational interpolant which
+    Doesn't do anything fancy, just a 9/8-degree rational interpolant which
     is accurate up to a couple of ulps in the (approximate) range [-8, 8],
     outside of which tanh(x) = +/-1 in single precision. The input is clamped
     to the range [-c, c]. The value c is chosen as the smallest value where
-    the approximation evaluates to exactly 1. In the reange [-0.0004, 0.0004]
-    the approximation tanh(x) ~= x is used for better accuracy as x tends to zero.
+    the approximation evaluates to exactly 1.
 
     This implementation works on both scalars and packets.
 */
 template <typename T>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS T ptanh_float(const T& a_x) {
-  // Clamp the inputs to the range [-c, c]
+  // Clamp the inputs to the range [-c, c] and set everything
+  // outside that range to 1.0. The value c is chosen as the smallest
+  // floating point argument such that the approximation is exactly 1.
+  // This saves clamping the value at the end.
 #ifdef EIGEN_VECTORIZE_FMA
-  const T plus_clamp = pset1<T>(7.99881172180175781f);
-  const T minus_clamp = pset1<T>(-7.99881172180175781f);
+  const T plus_clamp = pset1<T>(8.05359363555908203f);
+  const T minus_clamp = pset1<T>(-8.05359363555908203f);
 #else
-  const T plus_clamp = pset1<T>(7.90531110763549805f);
-  const T minus_clamp = pset1<T>(-7.90531110763549805f);
+  const T plus_clamp = pset1<T>(7.98551225662231445);
+  const T minus_clamp = pset1<T>(-7.98551225662231445);
 #endif
-  const T tiny = pset1<T>(0.0004f);
   const T x = pmax(pmin(a_x, plus_clamp), minus_clamp);
-  const T tiny_mask = pcmp_lt(pabs(a_x), tiny);
+
+  // The following rational approximation was generated by rminimax
+  // (https://gitlab.inria.fr/sfilip/rminimax) using the following
+  // command:
+  // $ ratapprox --function="tanh(x)" --dom='[-8.67,8.67]' --num="odd"
+  //   --den="even" --type="[9,8]" --numF="[SG]" --denF="[SG]" --log
+  //   --output=tanhf.sollya --dispCoeff="dec"
+
   // The monomial coefficients of the numerator polynomial (odd).
-  const T alpha_1 = pset1<T>(4.89352455891786e-03f);
-  const T alpha_3 = pset1<T>(6.37261928875436e-04f);
-  const T alpha_5 = pset1<T>(1.48572235717979e-05f);
-  const T alpha_7 = pset1<T>(5.12229709037114e-08f);
-  const T alpha_9 = pset1<T>(-8.60467152213735e-11f);
-  const T alpha_11 = pset1<T>(2.00018790482477e-13f);
-  const T alpha_13 = pset1<T>(-2.76076847742355e-16f);
+  const T alpha_3 = pset1<T>(1.340216100215911865234375e-1f);
+  const T alpha_5 = pset1<T>(3.52075672708451747894287109375e-3f);
+  const T alpha_7 = pset1<T>(2.10273356060497462749481201171875e-5f);
+  const T alpha_9 = pset1<T>(1.39455362813123429077677428722381591796875e-8f);
 
   // The monomial coefficients of the denominator polynomial (even).
-  const T beta_0 = pset1<T>(4.89352518554385e-03f);
-  const T beta_2 = pset1<T>(2.26843463243900e-03f);
-  const T beta_4 = pset1<T>(1.18534705686654e-04f);
-  const T beta_6 = pset1<T>(1.19825839466702e-06f);
+  const T beta_0 = pset1<T>(1.0f);
+  const T beta_2 = pset1<T>(4.67354834079742431640625e-1f);
+  const T beta_4 = pset1<T>(2.5972545146942138671875e-2f);
+  const T beta_6 = pset1<T>(3.326951409690082073211669921875e-4f);
+  const T beta_8 = pset1<T>(8.015776984393596649169921875e-7f);
 
   // Since the polynomials are odd/even, we need x^2.
   const T x2 = pmul(x, x);
+  const T x3 = pmul(x2, x);
 
-  // Evaluate the numerator polynomial p.
-  T p = pmadd(x2, alpha_13, alpha_11);
-  p = pmadd(x2, p, alpha_9);
-  p = pmadd(x2, p, alpha_7);
+  // Interleave the evaluation of the numerator polynomial p and
+  // denominator polynomial q.
+  T p = pmadd(x2, alpha_9, alpha_7);
+  T q = pmadd(x2, beta_8, beta_6);
   p = pmadd(x2, p, alpha_5);
+  q = pmadd(x2, q, beta_4);
   p = pmadd(x2, p, alpha_3);
-  p = pmadd(x2, p, alpha_1);
-  p = pmul(x, p);
-
-  // Evaluate the denominator polynomial q.
-  T q = pmadd(x2, beta_6, beta_4);
   q = pmadd(x2, q, beta_2);
+  // Take advantage of the fact that alpha_1 = 1 to compute
+  // x*(x^2*p + alpha_1) = x^3 * p + x.
+  p = pmadd(x3, p, x);
   q = pmadd(x2, q, beta_0);
 
   // Divide the numerator by the denominator.
-  return pselect(tiny_mask, x, pdiv(p, q));
+  return pdiv(p, q);
 }
 
 template <typename Packet>