diff --git a/manual/probes.texi b/manual/probes.texi
index e99b7f3cb4..ad673eb22b 100644
--- a/manual/probes.texi
+++ b/manual/probes.texi
@@ -258,20 +258,6 @@ Unless explicitly mentioned otherwise, a precision of 1 implies 24 bits of
 precision in the mantissa of the multiple precision number.  Hence, a precision
 level of 32 implies 768 bits of precision in the mantissa.
 
-@deftp Probe slowexp_p6 (double @var{$arg1}, double @var{$arg2})
-This probe is triggered when the @code{exp} function is called with an
-input that results in multiple precision computation with precision
-6.  Argument @var{$arg1} is the input value and @var{$arg2} is the
-computed output.
-@end deftp
-
-@deftp Probe slowexp_p32 (double @var{$arg1}, double @var{$arg2})
-This probe is triggered when the @code{exp} function is called with an
-input that results in multiple precision computation with precision
-32.  Argument @var{$arg1} is the input value and @var{$arg2} is the
-computed output.
-@end deftp
-
 @deftp Probe slowpow_p10 (double @var{$arg1}, double @var{$arg2}, double @var{$arg3}, double @var{$arg4})
 This probe is triggered when the @code{pow} function is called with
 inputs that result in multiple precision computation with precision
diff --git a/math/Makefile b/math/Makefile
index 4c8703c71e..46e33a6434 100644
--- a/math/Makefile
+++ b/math/Makefile
@@ -114,7 +114,7 @@ type-ldouble-yes := ldouble
 # double support
 type-double-suffix :=
 type-double-routines := branred doasin dosincos halfulp mpa mpatan2	\
-		       mpatan mpexp mplog mpsqrt mptan sincos32 slowexp	\
+		       mpatan mpexp mplog mpsqrt mptan sincos32	\
 		       slowpow sincostab k_rem_pio2
 
 # float support
diff --git a/sysdeps/generic/math_private.h b/sysdeps/generic/math_private.h
index 0a35cb39fb..f411188461 100644
--- a/sysdeps/generic/math_private.h
+++ b/sysdeps/generic/math_private.h
@@ -262,7 +262,6 @@ extern double __sin32 (double __x, double __res, double __res1);
 extern double __cos32 (double __x, double __res, double __res1);
 extern double __mpsin (double __x, double __dx, bool __range_reduce);
 extern double __mpcos (double __x, double __dx, bool __range_reduce);
-extern double __slowexp (double __x);
 extern double __slowpow (double __x, double __y, double __z);
 extern void __docos (double __x, double __dx, double __v[]);
 
diff --git a/sysdeps/i386/fpu/slowexp.c b/sysdeps/i386/fpu/slowexp.c
deleted file mode 100644
index 1cc8931700..0000000000
--- a/sysdeps/i386/fpu/slowexp.c
+++ /dev/null
@@ -1 +0,0 @@
-/* Not needed.  */
diff --git a/sysdeps/ia64/fpu/slowexp.c b/sysdeps/ia64/fpu/slowexp.c
deleted file mode 100644
index 1cc8931700..0000000000
--- a/sysdeps/ia64/fpu/slowexp.c
+++ /dev/null
@@ -1 +0,0 @@
-/* Not needed.  */
diff --git a/sysdeps/ieee754/dbl-64/e_exp.c b/sysdeps/ieee754/dbl-64/e_exp.c
index 3d2560c9c0..80e750c520 100644
--- a/sysdeps/ieee754/dbl-64/e_exp.c
+++ b/sysdeps/ieee754/dbl-64/e_exp.c
@@ -23,10 +23,10 @@
 /*           exp1                                                          */
 /*                                                                         */
 /* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h                       */
-/*              mpa.c mpexp.x slowexp.c                                    */
+/*              mpa.c mpexp.x                                              */
 /*                                                                         */
 /* An ultimate exp routine. Given an IEEE double machine number x          */
-/* it computes the correctly rounded (to nearest) value of e^x             */
+/* it computes an almost correctly rounded (to nearest) value of e^x       */
 /* Assumption: Machine arithmetic operations are performed in              */
 /* round to nearest mode of IEEE 754 standard.                             */
 /*                                                                         */
@@ -46,10 +46,6 @@
 # define SECTION
 #endif
 
-double __slowexp (double);
-
-/* An ultimate exp routine. Given an IEEE double machine number x it computes
-   the correctly rounded (to nearest) value of e^x.  */
 double
 SECTION
 __ieee754_exp (double x)
@@ -93,17 +89,10 @@ __ieee754_exp (double x)
 
 	rem = (bet + bet * eps) + al * eps;
 	res = al + rem;
-	cor = (al - res) + rem;
-	if (res == (res + cor * err_0))
-	  {
-	    retval = res * binexp.x;
-	    goto ret;
-	  }
-	else
-	  {
-	    retval = __slowexp (x);
-	    goto ret;
-	  }			/*if error is over bound */
+	/* Maximum relative error is 7.8e-22 (70.1 bits).
+	   Maximum ULP error is 0.500007.  */
+	retval = res * binexp.x;
+	goto ret;
       }
 
     if (n <= smallint)
@@ -166,38 +155,22 @@ __ieee754_exp (double x)
 	if (ex >= -1022)
 	  {
 	    binexp.i[HIGH_HALF] = (1023 + ex) << 20;
-	    if (res == (res + cor * err_0))
-	      {
-		retval = res * binexp.x;
-		goto ret;
-	      }
-	    else
-	      {
-		retval = __slowexp (x);
-		goto check_uflow_ret;
-	      }			/*if error is over bound */
+	    /* Does not underflow: res >= 1.0, binexp >= 0x1p-1022
+	       Maximum relative error is 7.8e-22 (70.1 bits).
+	       Maximum ULP error is 0.500007.  */
+	    retval = res * binexp.x;
+	    goto ret;
 	  }
 	ex = -(1022 + ex);
 	binexp.i[HIGH_HALF] = (1023 - ex) << 20;
 	res *= binexp.x;
 	cor *= binexp.x;
-	eps = 1.0000000001 + err_0 * binexp.x;
 	t = 1.0 + res;
 	y = ((1.0 - t) + res) + cor;
 	res = t + y;
-	cor = (t - res) + y;
-	if (res == (res + eps * cor))
-	  {
-	    binexp.i[HIGH_HALF] = 0x00100000;
-	    retval = (res - 1.0) * binexp.x;
-	    goto check_uflow_ret;
-	  }
-	else
-	  {
-	    retval = __slowexp (x);
-	    goto check_uflow_ret;
-	  }			/*   if error is over bound    */
-      check_uflow_ret:
+	/* Maximum ULP error is 0.5000035.  */
+	binexp.i[HIGH_HALF] = 0x00100000;
+	retval = (res - 1.0) * binexp.x;
 	if (retval < DBL_MIN)
 	  {
 	    double force_underflow = tiny * tiny;
@@ -210,10 +183,9 @@ __ieee754_exp (double x)
     else
       {
 	binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 767) << 20;
-	if (res == (res + cor * err_0))
-	  retval = res * binexp.x * t256.x;
-	else
-	  retval = __slowexp (x);
+	/* Maximum relative error is 7.8e-22 (70.1 bits).
+	   Maximum ULP error is 0.500007.  */
+	retval = res * binexp.x * t256.x;
 	if (isinf (retval))
 	  goto ret_huge;
 	else
diff --git a/sysdeps/ieee754/dbl-64/e_pow.c b/sysdeps/ieee754/dbl-64/e_pow.c
index f6e5fcdbce..c410b04e3e 100644
--- a/sysdeps/ieee754/dbl-64/e_pow.c
+++ b/sysdeps/ieee754/dbl-64/e_pow.c
@@ -25,7 +25,7 @@
 /*             log1                                                        */
 /*             checkint                                                    */
 /* FILES NEEDED: dla.h endian.h mpa.h mydefs.h                             */
-/*               halfulp.c mpexp.c mplog.c slowexp.c slowpow.c mpa.c       */
+/*               halfulp.c mpexp.c mplog.c slowpow.c mpa.c                 */
 /*                          uexp.c  upow.c				   */
 /*               root.tbl uexp.tbl upow.tbl                                */
 /* An ultimate power routine. Given two IEEE double machine numbers y,x    */
diff --git a/sysdeps/ieee754/dbl-64/slowexp.c b/sysdeps/ieee754/dbl-64/slowexp.c
deleted file mode 100644
index ba5617466c..0000000000
--- a/sysdeps/ieee754/dbl-64/slowexp.c
+++ /dev/null
@@ -1,86 +0,0 @@
-/*
- * IBM Accurate Mathematical Library
- * written by International Business Machines Corp.
- * Copyright (C) 2001-2018 Free Software Foundation, Inc.
- *
- * This program is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Lesser General Public License as published by
- * the Free Software Foundation; either version 2.1 of the License, or
- * (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU Lesser General Public License for more details.
- *
- * You should have received a copy of the GNU Lesser General Public License
- * along with this program; if not, see <http://www.gnu.org/licenses/>.
- */
-/**************************************************************************/
-/*  MODULE_NAME:slowexp.c                                                 */
-/*                                                                        */
-/*  FUNCTION:slowexp                                                      */
-/*                                                                        */
-/*  FILES NEEDED:mpa.h                                                    */
-/*               mpa.c mpexp.c                                            */
-/*                                                                        */
-/*Converting from double precision to Multi-precision and calculating     */
-/* e^x                                                                    */
-/**************************************************************************/
-#include <math_private.h>
-
-#include <stap-probe.h>
-
-#ifndef USE_LONG_DOUBLE_FOR_MP
-# include "mpa.h"
-void __mpexp (mp_no *x, mp_no *y, int p);
-#endif
-
-#ifndef SECTION
-# define SECTION
-#endif
-
-/*Converting from double precision to Multi-precision and calculating  e^x */
-double
-SECTION
-__slowexp (double x)
-{
-#ifndef USE_LONG_DOUBLE_FOR_MP
-  double w, z, res, eps = 3.0e-26;
-  int p;
-  mp_no mpx, mpy, mpz, mpw, mpeps, mpcor;
-
-  /* Use the multiple precision __MPEXP function to compute the exponential
-     First at 144 bits and if it is not accurate enough, at 768 bits.  */
-  p = 6;
-  __dbl_mp (x, &mpx, p);
-  __mpexp (&mpx, &mpy, p);
-  __dbl_mp (eps, &mpeps, p);
-  __mul (&mpeps, &mpy, &mpcor, p);
-  __add (&mpy, &mpcor, &mpw, p);
-  __sub (&mpy, &mpcor, &mpz, p);
-  __mp_dbl (&mpw, &w, p);
-  __mp_dbl (&mpz, &z, p);
-  if (w == z)
-    {
-      /* Track how often we get to the slow exp code plus
-	 its input/output values.  */
-      LIBC_PROBE (slowexp_p6, 2, &x, &w);
-      return w;
-    }
-  else
-    {
-      p = 32;
-      __dbl_mp (x, &mpx, p);
-      __mpexp (&mpx, &mpy, p);
-      __mp_dbl (&mpy, &res, p);
-
-      /* Track how often we get to the uber-slow exp code plus
-	 its input/output values.  */
-      LIBC_PROBE (slowexp_p32, 2, &x, &res);
-      return res;
-    }
-#else
-  return (double) __ieee754_expl((long double)x);
-#endif
-}
diff --git a/sysdeps/ieee754/dbl-64/uexp.h b/sysdeps/ieee754/dbl-64/uexp.h
index a8a023ee80..592b9725b9 100644
--- a/sysdeps/ieee754/dbl-64/uexp.h
+++ b/sysdeps/ieee754/dbl-64/uexp.h
@@ -30,7 +30,7 @@
 #include "mydefs.h"
 
 const static double zero = 0.0, hhuge = 1.0e300, tiny = 1.0e-300,
-err_0 = 1.000014, err_1 = 0.000016;
+err_1 = 0.000016;
 const static int4 bigint = 0x40862002,
              badint = 0x40876000,smallint = 0x3C8fffff;
 const static int4 hugeint = 0x7FFFFFFF, infint = 0x7ff00000;
diff --git a/sysdeps/m68k/m680x0/fpu/slowexp.c b/sysdeps/m68k/m680x0/fpu/slowexp.c
deleted file mode 100644
index 1cc8931700..0000000000
--- a/sysdeps/m68k/m680x0/fpu/slowexp.c
+++ /dev/null
@@ -1 +0,0 @@
-/* Not needed.  */
diff --git a/sysdeps/powerpc/power4/fpu/Makefile b/sysdeps/powerpc/power4/fpu/Makefile
index e17d32f30e..ded9976b9d 100644
--- a/sysdeps/powerpc/power4/fpu/Makefile
+++ b/sysdeps/powerpc/power4/fpu/Makefile
@@ -3,5 +3,4 @@
 ifeq ($(subdir),math)
 CFLAGS-mpa.c += --param max-unroll-times=4 -funroll-loops -fpeel-loops
 CPPFLAGS-slowpow.c += -DUSE_LONG_DOUBLE_FOR_MP=1
-CPPFLAGS-slowexp.c += -DUSE_LONG_DOUBLE_FOR_MP=1
 endif
diff --git a/sysdeps/x86_64/fpu/multiarch/Makefile b/sysdeps/x86_64/fpu/multiarch/Makefile
index 9a89bfc286..6935ac3dd0 100644
--- a/sysdeps/x86_64/fpu/multiarch/Makefile
+++ b/sysdeps/x86_64/fpu/multiarch/Makefile
@@ -10,7 +10,7 @@ libm-sysdep_routines += s_ceil-sse4_1 s_ceilf-sse4_1 s_floor-sse4_1 \
 
 libm-sysdep_routines += e_exp-fma e_log-fma e_pow-fma s_atan-fma \
 			e_asin-fma e_atan2-fma s_sin-fma s_tan-fma \
-			mplog-fma mpa-fma slowexp-fma slowpow-fma \
+			mplog-fma mpa-fma slowpow-fma \
 			sincos32-fma doasin-fma dosincos-fma \
 			halfulp-fma mpexp-fma \
 			mpatan2-fma mpatan-fma mpsqrt-fma mptan-fma
@@ -32,7 +32,6 @@ CFLAGS-mpsqrt-fma.c = -mfma -mavx2
 CFLAGS-mptan-fma.c = -mfma -mavx2
 CFLAGS-s_atan-fma.c = -mfma -mavx2
 CFLAGS-sincos32-fma.c = -mfma -mavx2
-CFLAGS-slowexp-fma.c = -mfma -mavx2
 CFLAGS-slowpow-fma.c = -mfma -mavx2
 CFLAGS-s_sin-fma.c = -mfma -mavx2
 CFLAGS-s_tan-fma.c = -mfma -mavx2
@@ -53,7 +52,7 @@ CFLAGS-s_sincosf-fma.c = -mfma -mavx2
 
 libm-sysdep_routines += e_exp-fma4 e_log-fma4 e_pow-fma4 s_atan-fma4 \
 			e_asin-fma4 e_atan2-fma4 s_sin-fma4 s_tan-fma4 \
-			mplog-fma4 mpa-fma4 slowexp-fma4 slowpow-fma4 \
+			mplog-fma4 mpa-fma4 slowpow-fma4 \
 			sincos32-fma4 doasin-fma4 dosincos-fma4 \
 			halfulp-fma4 mpexp-fma4 \
 			mpatan2-fma4 mpatan-fma4 mpsqrt-fma4 mptan-fma4
@@ -75,14 +74,13 @@ CFLAGS-mpsqrt-fma4.c = -mfma4
 CFLAGS-mptan-fma4.c = -mfma4
 CFLAGS-s_atan-fma4.c = -mfma4
 CFLAGS-sincos32-fma4.c = -mfma4
-CFLAGS-slowexp-fma4.c = -mfma4
 CFLAGS-slowpow-fma4.c = -mfma4
 CFLAGS-s_sin-fma4.c = -mfma4
 CFLAGS-s_tan-fma4.c = -mfma4
 
 libm-sysdep_routines += e_exp-avx e_log-avx s_atan-avx \
 			e_atan2-avx s_sin-avx s_tan-avx \
-			mplog-avx mpa-avx slowexp-avx \
+			mplog-avx mpa-avx \
 			mpexp-avx
 
 CFLAGS-e_atan2-avx.c = -msse2avx -DSSE2AVX
@@ -93,7 +91,6 @@ CFLAGS-mpexp-avx.c = -msse2avx -DSSE2AVX
 CFLAGS-mplog-avx.c = -msse2avx -DSSE2AVX
 CFLAGS-s_atan-avx.c = -msse2avx -DSSE2AVX
 CFLAGS-s_sin-avx.c = -msse2avx -DSSE2AVX
-CFLAGS-slowexp-avx.c = -msse2avx -DSSE2AVX
 CFLAGS-s_tan-avx.c = -msse2avx -DSSE2AVX
 endif
 
diff --git a/sysdeps/x86_64/fpu/multiarch/e_exp-avx.c b/sysdeps/x86_64/fpu/multiarch/e_exp-avx.c
index ee5dd6d2dc..afd917442a 100644
--- a/sysdeps/x86_64/fpu/multiarch/e_exp-avx.c
+++ b/sysdeps/x86_64/fpu/multiarch/e_exp-avx.c
@@ -1,6 +1,5 @@
 #define __ieee754_exp __ieee754_exp_avx
 #define __exp1 __exp1_avx
-#define __slowexp __slowexp_avx
 #define SECTION __attribute__ ((section (".text.avx")))
 
 #include <sysdeps/ieee754/dbl-64/e_exp.c>
diff --git a/sysdeps/x86_64/fpu/multiarch/e_exp-fma.c b/sysdeps/x86_64/fpu/multiarch/e_exp-fma.c
index 6e0fdb7941..765b1b9dd3 100644
--- a/sysdeps/x86_64/fpu/multiarch/e_exp-fma.c
+++ b/sysdeps/x86_64/fpu/multiarch/e_exp-fma.c
@@ -1,6 +1,5 @@
 #define __ieee754_exp __ieee754_exp_fma
 #define __exp1 __exp1_fma
-#define __slowexp __slowexp_fma
 #define SECTION __attribute__ ((section (".text.fma")))
 
 #include <sysdeps/ieee754/dbl-64/e_exp.c>
diff --git a/sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c b/sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c
index ae6eb67603..9ac7acad28 100644
--- a/sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c
+++ b/sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c
@@ -1,6 +1,5 @@
 #define __ieee754_exp __ieee754_exp_fma4
 #define __exp1 __exp1_fma4
-#define __slowexp __slowexp_fma4
 #define SECTION __attribute__ ((section (".text.fma4")))
 
 #include <sysdeps/ieee754/dbl-64/e_exp.c>
diff --git a/sysdeps/x86_64/fpu/multiarch/slowexp-avx.c b/sysdeps/x86_64/fpu/multiarch/slowexp-avx.c
deleted file mode 100644
index d01c6d71a4..0000000000
--- a/sysdeps/x86_64/fpu/multiarch/slowexp-avx.c
+++ /dev/null
@@ -1,9 +0,0 @@
-#define __slowexp __slowexp_avx
-#define __add __add_avx
-#define __dbl_mp __dbl_mp_avx
-#define __mpexp __mpexp_avx
-#define __mul __mul_avx
-#define __sub __sub_avx
-#define SECTION __attribute__ ((section (".text.avx")))
-
-#include <sysdeps/ieee754/dbl-64/slowexp.c>
diff --git a/sysdeps/x86_64/fpu/multiarch/slowexp-fma.c b/sysdeps/x86_64/fpu/multiarch/slowexp-fma.c
deleted file mode 100644
index 6fffca1a93..0000000000
--- a/sysdeps/x86_64/fpu/multiarch/slowexp-fma.c
+++ /dev/null
@@ -1,9 +0,0 @@
-#define __slowexp __slowexp_fma
-#define __add __add_fma
-#define __dbl_mp __dbl_mp_fma
-#define __mpexp __mpexp_fma
-#define __mul __mul_fma
-#define __sub __sub_fma
-#define SECTION __attribute__ ((section (".text.fma")))
-
-#include <sysdeps/ieee754/dbl-64/slowexp.c>
diff --git a/sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c b/sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c
deleted file mode 100644
index 3bcde84233..0000000000
--- a/sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c
+++ /dev/null
@@ -1,9 +0,0 @@
-#define __slowexp __slowexp_fma4
-#define __add __add_fma4
-#define __dbl_mp __dbl_mp_fma4
-#define __mpexp __mpexp_fma4
-#define __mul __mul_fma4
-#define __sub __sub_fma4
-#define SECTION __attribute__ ((section (".text.fma4")))
-
-#include <sysdeps/ieee754/dbl-64/slowexp.c>
