expq3 (problem 3.4.2)

Percentage Accurate: 0.0% → 99.8%

Time: 33.6s

Alternatives: 1

Speedup: N/A×

Specification

\[\left(\left|a\right| \leq 710 \land \left|b\right| \leq 710\right) \land \left(10^{-27} \cdot \mathsf{min}\left(\left|a\right|, \left|b\right|\right) \leq \varepsilon \land \varepsilon \leq \mathsf{min}\left(\left|a\right|, \left|b\right|\right)\right)\]

Math

\[\begin{array}{l} \\ \frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)} \end{array} \]

FPCore

(FPCore (a b eps)
 :precision binary64
 (/
  (* eps (- (exp (* (+ a b) eps)) 1.0))
  (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))))

C

double code(double a, double b, double eps) {
	return (eps * (exp(((a + b) * eps)) - 1.0)) / ((exp((a * eps)) - 1.0) * (exp((b * eps)) - 1.0));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(a, b, eps)
use fmin_fmax_functions
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: eps
    code = (eps * (exp(((a + b) * eps)) - 1.0d0)) / ((exp((a * eps)) - 1.0d0) * (exp((b * eps)) - 1.0d0))
end function

Java

public static double code(double a, double b, double eps) {
	return (eps * (Math.exp(((a + b) * eps)) - 1.0)) / ((Math.exp((a * eps)) - 1.0) * (Math.exp((b * eps)) - 1.0));
}

Python

def code(a, b, eps):
	return (eps * (math.exp(((a + b) * eps)) - 1.0)) / ((math.exp((a * eps)) - 1.0) * (math.exp((b * eps)) - 1.0))

Julia

function code(a, b, eps)
	return Float64(Float64(eps * Float64(exp(Float64(Float64(a + b) * eps)) - 1.0)) / Float64(Float64(exp(Float64(a * eps)) - 1.0) * Float64(exp(Float64(b * eps)) - 1.0)))
end

MATLAB

function tmp = code(a, b, eps)
	tmp = (eps * (exp(((a + b) * eps)) - 1.0)) / ((exp((a * eps)) - 1.0) * (exp((b * eps)) - 1.0));
end

Wolfram

code[a_, b_, eps_] := N[(N[(eps * N[(N[Exp[N[(N[(a + b), $MachinePrecision] * eps), $MachinePrecision]], $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / N[(N[(N[Exp[N[(a * eps), $MachinePrecision]], $MachinePrecision] - 1.0), $MachinePrecision] * N[(N[Exp[N[(b * eps), $MachinePrecision]], $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 0.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)} \end{array} \]

FPCore

(FPCore (a b eps)
 :precision binary64
 (/
  (* eps (- (exp (* (+ a b) eps)) 1.0))
  (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))))

C

double code(double a, double b, double eps) {
	return (eps * (exp(((a + b) * eps)) - 1.0)) / ((exp((a * eps)) - 1.0) * (exp((b * eps)) - 1.0));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(a, b, eps)
use fmin_fmax_functions
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: eps
    code = (eps * (exp(((a + b) * eps)) - 1.0d0)) / ((exp((a * eps)) - 1.0d0) * (exp((b * eps)) - 1.0d0))
end function

Java

public static double code(double a, double b, double eps) {
	return (eps * (Math.exp(((a + b) * eps)) - 1.0)) / ((Math.exp((a * eps)) - 1.0) * (Math.exp((b * eps)) - 1.0));
}

Python

def code(a, b, eps):
	return (eps * (math.exp(((a + b) * eps)) - 1.0)) / ((math.exp((a * eps)) - 1.0) * (math.exp((b * eps)) - 1.0))

Julia

function code(a, b, eps)
	return Float64(Float64(eps * Float64(exp(Float64(Float64(a + b) * eps)) - 1.0)) / Float64(Float64(exp(Float64(a * eps)) - 1.0) * Float64(exp(Float64(b * eps)) - 1.0)))
end

MATLAB

function tmp = code(a, b, eps)
	tmp = (eps * (exp(((a + b) * eps)) - 1.0)) / ((exp((a * eps)) - 1.0) * (exp((b * eps)) - 1.0));
end

Wolfram

code[a_, b_, eps_] := N[(N[(eps * N[(N[Exp[N[(N[(a + b), $MachinePrecision] * eps), $MachinePrecision]], $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / N[(N[(N[Exp[N[(a * eps), $MachinePrecision]], $MachinePrecision] - 1.0), $MachinePrecision] * N[(N[Exp[N[(b * eps), $MachinePrecision]], $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, N/A× speedup

Math

\[\begin{array}{l} [a, b, eps] = \mathsf{sort}([a, b, eps])\\ \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.16666666666666666, a, 0.25 \cdot a\right)\\ t_1 := 0.5 \cdot a - t\_0\\ t_2 := 0.16666666666666666 \cdot \left(a \cdot a\right) - \mathsf{fma}\left(0.041666666666666664, a \cdot a, \mathsf{fma}\left(0.08333333333333333, a \cdot a, 0.5 \cdot \left(a \cdot t\_1\right)\right)\right)\\ t_3 := \left(a \cdot a\right) \cdot a\\ \frac{1 + \mathsf{fma}\left(\varepsilon \cdot \varepsilon, \mathsf{fma}\left(b, \mathsf{fma}\left(0.08333333333333333, b, 0.5 \cdot a\right) - t\_0, \varepsilon \cdot \mathsf{fma}\left(b, \varepsilon \cdot \left(0.041666666666666664 \cdot t\_3 - \mathsf{fma}\left(0.008333333333333333, t\_3, \mathsf{fma}\left(0.020833333333333332, t\_3, \mathsf{fma}\left(0.16666666666666666, \left(a \cdot a\right) \cdot t\_1, 0.5 \cdot \left(a \cdot t\_2\right)\right)\right)\right)\right), b \cdot t\_2\right)\right), \frac{b}{a}\right)}{b} \end{array} \end{array} \]

FPCore

NOTE: a, b, and eps should be sorted in increasing order before calling this function.
(FPCore (a b eps)
 :precision binary64
 (let* ((t_0 (fma 0.16666666666666666 a (* 0.25 a)))
        (t_1 (- (* 0.5 a) t_0))
        (t_2
         (-
          (* 0.16666666666666666 (* a a))
          (fma
           0.041666666666666664
           (* a a)
           (fma 0.08333333333333333 (* a a) (* 0.5 (* a t_1))))))
        (t_3 (* (* a a) a)))
   (/
    (+
     1.0
     (fma
      (* eps eps)
      (fma
       b
       (- (fma 0.08333333333333333 b (* 0.5 a)) t_0)
       (*
        eps
        (fma
         b
         (*
          eps
          (-
           (* 0.041666666666666664 t_3)
           (fma
            0.008333333333333333
            t_3
            (fma
             0.020833333333333332
             t_3
             (fma 0.16666666666666666 (* (* a a) t_1) (* 0.5 (* a t_2)))))))
         (* b t_2))))
      (/ b a)))
    b)))

C

assert(a < b && b < eps);
double code(double a, double b, double eps) {
	double t_0 = fma(0.16666666666666666, a, (0.25 * a));
	double t_1 = (0.5 * a) - t_0;
	double t_2 = (0.16666666666666666 * (a * a)) - fma(0.041666666666666664, (a * a), fma(0.08333333333333333, (a * a), (0.5 * (a * t_1))));
	double t_3 = (a * a) * a;
	return (1.0 + fma((eps * eps), fma(b, (fma(0.08333333333333333, b, (0.5 * a)) - t_0), (eps * fma(b, (eps * ((0.041666666666666664 * t_3) - fma(0.008333333333333333, t_3, fma(0.020833333333333332, t_3, fma(0.16666666666666666, ((a * a) * t_1), (0.5 * (a * t_2))))))), (b * t_2)))), (b / a))) / b;
}

Julia

a, b, eps = sort([a, b, eps])
function code(a, b, eps)
	t_0 = fma(0.16666666666666666, a, Float64(0.25 * a))
	t_1 = Float64(Float64(0.5 * a) - t_0)
	t_2 = Float64(Float64(0.16666666666666666 * Float64(a * a)) - fma(0.041666666666666664, Float64(a * a), fma(0.08333333333333333, Float64(a * a), Float64(0.5 * Float64(a * t_1)))))
	t_3 = Float64(Float64(a * a) * a)
	return Float64(Float64(1.0 + fma(Float64(eps * eps), fma(b, Float64(fma(0.08333333333333333, b, Float64(0.5 * a)) - t_0), Float64(eps * fma(b, Float64(eps * Float64(Float64(0.041666666666666664 * t_3) - fma(0.008333333333333333, t_3, fma(0.020833333333333332, t_3, fma(0.16666666666666666, Float64(Float64(a * a) * t_1), Float64(0.5 * Float64(a * t_2))))))), Float64(b * t_2)))), Float64(b / a))) / b)
end

Wolfram

NOTE: a, b, and eps should be sorted in increasing order before calling this function.
code[a_, b_, eps_] := Block[{t$95$0 = N[(0.16666666666666666 * a + N[(0.25 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.5 * a), $MachinePrecision] - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(0.16666666666666666 * N[(a * a), $MachinePrecision]), $MachinePrecision] - N[(0.041666666666666664 * N[(a * a), $MachinePrecision] + N[(0.08333333333333333 * N[(a * a), $MachinePrecision] + N[(0.5 * N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * a), $MachinePrecision] * a), $MachinePrecision]}, N[(N[(1.0 + N[(N[(eps * eps), $MachinePrecision] * N[(b * N[(N[(0.08333333333333333 * b + N[(0.5 * a), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] + N[(eps * N[(b * N[(eps * N[(N[(0.041666666666666664 * t$95$3), $MachinePrecision] - N[(0.008333333333333333 * t$95$3 + N[(0.020833333333333332 * t$95$3 + N[(0.16666666666666666 * N[(N[(a * a), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(0.5 * N[(a * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Initial program 0.0%

   \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)} \]
2. Add Preprocessing

3. Taylor expanded in b around 0

   \[\leadsto \color{blue}{\frac{1 + b \cdot \left(\left(b \cdot \left(\left(\frac{1}{2} \cdot \frac{{\varepsilon}^{2} \cdot e^{a \cdot \varepsilon}}{e^{a \cdot \varepsilon} - 1} + b \cdot \left(\frac{1}{6} \cdot \frac{{\varepsilon}^{3} \cdot e^{a \cdot \varepsilon}}{e^{a \cdot \varepsilon} - 1} - \left(\frac{1}{24} \cdot {\varepsilon}^{3} + \left(\frac{1}{6} \cdot \left({\varepsilon}^{2} \cdot \left(\frac{\varepsilon \cdot e^{a \cdot \varepsilon}}{e^{a \cdot \varepsilon} - 1} - \frac{1}{2} \cdot \varepsilon\right)\right) + \frac{1}{2} \cdot \left(\varepsilon \cdot \left(\frac{1}{2} \cdot \frac{{\varepsilon}^{2} \cdot e^{a \cdot \varepsilon}}{e^{a \cdot \varepsilon} - 1} - \left(\frac{1}{6} \cdot {\varepsilon}^{2} + \frac{1}{2} \cdot \left(\varepsilon \cdot \left(\frac{\varepsilon \cdot e^{a \cdot \varepsilon}}{e^{a \cdot \varepsilon} - 1} - \frac{1}{2} \cdot \varepsilon\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(\frac{1}{6} \cdot {\varepsilon}^{2} + \frac{1}{2} \cdot \left(\varepsilon \cdot \left(\frac{\varepsilon \cdot e^{a \cdot \varepsilon}}{e^{a \cdot \varepsilon} - 1} - \frac{1}{2} \cdot \varepsilon\right)\right)\right)\right) + \frac{\varepsilon \cdot e^{a \cdot \varepsilon}}{e^{a \cdot \varepsilon} - 1}\right) - \frac{1}{2} \cdot \varepsilon\right)}{b}} \]

5. Applied rewrites 37.0%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(\varepsilon \cdot \varepsilon\right) \cdot \varepsilon\right) \cdot {\left(e^{a}\right)}^{\varepsilon}}{\mathsf{expm1}\left(a \cdot \varepsilon\right)} \cdot 0.16666666666666666 - 0.041666666666666664 \cdot \left(\left(\varepsilon \cdot \varepsilon\right) \cdot \varepsilon\right)\right) - \mathsf{fma}\left(\left(\left(\frac{\left(\left(\varepsilon \cdot \varepsilon\right) \cdot 0.5\right) \cdot {\left(e^{a}\right)}^{\varepsilon}}{\mathsf{expm1}\left(a \cdot \varepsilon\right)} - 0.16666666666666666 \cdot \left(\varepsilon \cdot \varepsilon\right)\right) - \left(0.5 \cdot \varepsilon\right) \cdot \mathsf{fma}\left(\varepsilon, \frac{{\left(e^{a}\right)}^{\varepsilon}}{\mathsf{expm1}\left(a \cdot \varepsilon\right)}, -0.5 \cdot \varepsilon\right)\right) \cdot \varepsilon, 0.5, \left(0.16666666666666666 \cdot \left(\varepsilon \cdot \varepsilon\right)\right) \cdot \mathsf{fma}\left(\varepsilon, \frac{{\left(e^{a}\right)}^{\varepsilon}}{\mathsf{expm1}\left(a \cdot \varepsilon\right)}, -0.5 \cdot \varepsilon\right)\right), b, \frac{\left(\left(\varepsilon \cdot \varepsilon\right) \cdot 0.5\right) \cdot {\left(e^{a}\right)}^{\varepsilon}}{\mathsf{expm1}\left(a \cdot \varepsilon\right)}\right) - \mathsf{fma}\left(0.5 \cdot \varepsilon, \mathsf{fma}\left(\varepsilon, \frac{{\left(e^{a}\right)}^{\varepsilon}}{\mathsf{expm1}\left(a \cdot \varepsilon\right)}, -0.5 \cdot \varepsilon\right), 0.16666666666666666 \cdot \left(\varepsilon \cdot \varepsilon\right)\right), b, \mathsf{fma}\left(\varepsilon, \frac{{\left(e^{a}\right)}^{\varepsilon}}{\mathsf{expm1}\left(a \cdot \varepsilon\right)}, -0.5 \cdot \varepsilon\right)\right), b, 1\right)}{b}} \]

6. Taylor expanded in eps around 0

   \[\leadsto \frac{1 + \left({\varepsilon}^{2} \cdot \left(b \cdot \left(\left(\frac{1}{12} \cdot b + \frac{1}{2} \cdot a\right) - \left(\frac{1}{6} \cdot a + \frac{1}{4} \cdot a\right)\right) + \varepsilon \cdot \left(b \cdot \left(\varepsilon \cdot \left(\frac{1}{24} \cdot {a}^{3} - \left(\frac{1}{120} \cdot {a}^{3} + \left(\frac{1}{48} \cdot {a}^{3} + \left(\frac{1}{6} \cdot \left({a}^{2} \cdot \left(\frac{1}{2} \cdot a - \left(\frac{1}{6} \cdot a + \frac{1}{4} \cdot a\right)\right)\right) + \frac{1}{2} \cdot \left(a \cdot \left(\frac{1}{6} \cdot {a}^{2} - \left(\frac{1}{24} \cdot {a}^{2} + \left(\frac{1}{12} \cdot {a}^{2} + \frac{1}{2} \cdot \left(a \cdot \left(\frac{1}{2} \cdot a - \left(\frac{1}{6} \cdot a + \frac{1}{4} \cdot a\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) + b \cdot \left(\frac{1}{6} \cdot {a}^{2} - \left(\frac{1}{24} \cdot {a}^{2} + \left(\frac{1}{12} \cdot {a}^{2} + \frac{1}{2} \cdot \left(a \cdot \left(\frac{1}{2} \cdot a - \left(\frac{1}{6} \cdot a + \frac{1}{4} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) + \frac{b}{a}\right)}{b} \]

8. Applied rewrites 99.8%

   \[\leadsto \frac{1 + \mathsf{fma}\left(\varepsilon \cdot \varepsilon, \mathsf{fma}\left(b, \mathsf{fma}\left(0.08333333333333333, b, 0.5 \cdot a\right) - \mathsf{fma}\left(0.16666666666666666, a, 0.25 \cdot a\right), \varepsilon \cdot \mathsf{fma}\left(b, \varepsilon \cdot \left(0.041666666666666664 \cdot \left(\left(a \cdot a\right) \cdot a\right) - \mathsf{fma}\left(0.008333333333333333, \left(a \cdot a\right) \cdot a, \mathsf{fma}\left(0.020833333333333332, \left(a \cdot a\right) \cdot a, \mathsf{fma}\left(0.16666666666666666, \left(a \cdot a\right) \cdot \left(0.5 \cdot a - \mathsf{fma}\left(0.16666666666666666, a, 0.25 \cdot a\right)\right), 0.5 \cdot \left(a \cdot \left(0.16666666666666666 \cdot \left(a \cdot a\right) - \mathsf{fma}\left(0.041666666666666664, a \cdot a, \mathsf{fma}\left(0.08333333333333333, a \cdot a, 0.5 \cdot \left(a \cdot \left(0.5 \cdot a - \mathsf{fma}\left(0.16666666666666666, a, 0.25 \cdot a\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right), b \cdot \left(0.16666666666666666 \cdot \left(a \cdot a\right) - \mathsf{fma}\left(0.041666666666666664, a \cdot a, \mathsf{fma}\left(0.08333333333333333, a \cdot a, 0.5 \cdot \left(a \cdot \left(0.5 \cdot a - \mathsf{fma}\left(0.16666666666666666, a, 0.25 \cdot a\right)\right)\right)\right)\right)\right)\right)\right), \frac{b}{a}\right)}{b} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2025065 
(FPCore (a b eps)
  :name "expq3 (problem 3.4.2)"
  :precision binary64
  :pre (and (and (<= (fabs a) 710.0) (<= (fabs b) 710.0)) (and (<= (* 1e-27 (fmin (fabs a) (fabs b))) eps) (<= eps (fmin (fabs a) (fabs b)))))

  :alt
  (! :herbie-platform c (+ (/ 1 a) (/ 1 b)))

  (/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))))