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The clock cycle count for "expf()" (reference) is 141645.

The clock cycle count for "expapprox()" is 74.

The clock cycle count for "expapprox4()" is 127 (/4 = 31).

// GCC
#define RESTRICT __restrict__

// Disable range check makes faster evaluation of exp().

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// code From http://gallium.inria.fr/blog/fast-vectorizable-math-approx/

$ e-gcc compile options: -O3 -mno-soft-cmpsf -mcmove -mfp-mode=truncate

// 73 clocks
00000f40 <_expapprox>:
     f40:       200b 0002       mov r1,0x0
     f44:       476b 0aa2       mov r2,0xaa3b
     f48:       470b 14b2       movt r2,0x4b38
     f4c:       2fcb 14e2       movt r1,0x4e7e

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#include <cmath>
#include <emmintrin.h>

#define _mm_set1_pd(x) _mm_set_pd((x), (x))

#define FORCE_INLINE    __attriabute__((force_inline))

// Compute exp(x) using trigonometric function.
inline __m128d exp_tri(__m128d v)
{

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_ZN5fmath3expEd:
.LLFB2:
.L46:
.LSSN28:

/*    167 */	add	%sp,-208,%sp


.L47:
.LSSN29:

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# K frontend
$ FCCpx -Kfast,nounroll,noswp exp_bench.cpp fmath.cpp
exp_bench.cpp:
fmath.cpp:
"fmath.cpp", line 30: warning: variable "fmath::local::LOG_TABLE_SIZE" was declared but never referenced
  const size_t LOG_TABLE_SIZE = 12;
               ^

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L21:
.LSSN2:

/*     12 */    frcpad  %f0,%f32

/*     12 */    sethi   %h44(.LR0),%g1

/*     12 */    or      %g1,%m44(.LR0),%g1

/*     12 */    sllx    %g1,12,%g1

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PRE_ALIGN(128) struct __vec8_d { 
    __vec8_d() { }

    FORCEINLINE __vec8_d(const double v0) {
        u.v0 = _mm_set_pd(v0, v0);
        u.v1 = _mm_set_pd(v0, v0);
        u.v2 = _mm_set_pd(v0, v0);
        u.v3 = _mm_set_pd(v0, v0);
    }

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#include <cstdio>
#include <cmath>
#include <emmintrin.h>

#define _mm_set1_pd(x) _mm_set_pd((x), (x))

// Probably somewhat faster.
inline __m128d fastexp(__m128d v)
{
  const __m128d inv_log2 = _mm_set1_pd(1.4426950408889634073599);

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// Based on glsl-sse2
inline __m128d mylog2(const __m128d v) {
    int ibuf[4];
    __m128d o = _mm_set_pd(1.0, 1.0);
    __m128i infVal = _mm_set_epi32(0x7FF00000, 0x00000000, 0x7FF00000, 0x00000000);
    __m128d c = *(reinterpret_cast<__m128d*>(&infVal));
    __m128d f = _mm_sub_pd(_mm_or_pd(_mm_andnot_pd(c, v),
                                     _mm_and_pd(c, o)), o);
    //const __m128i iVal = *(reinterpret_cast<const __m128i*>(&v));
    //__m128i a = _mm_sub_epi32(_mm_srli_epi32(iVal, 20),

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#include <cstdio>
#include <cmath>
#include <emmintrin.h>

#define _mm_set1_pd(x) _mm_set_pd((x), (x))


// Based on http://www.chokkan.org/blog/archives/340
inline __m128d myexp(__m128d v)
{