Average Error: 0.6 → 0.5
Time: 2.8s
Precision: binary64
\[\frac{e^{a}}{e^{a} + e^{b}} \]
↓
\[{\left(e^{\log \left(e^{a} + e^{b}\right) - a}\right)}^{-1} \]
(FPCore (a b) :precision binary64 (/ (exp a) (+ (exp a) (exp b))))
↓
(FPCore (a b)
 :precision binary64
 (pow (exp (- (log (+ (exp a) (exp b))) a)) -1.0))
double code(double a, double b) {
	return exp(a) / (exp(a) + exp(b));
}
↓
double code(double a, double b) {
	return pow(exp((log((exp(a) + exp(b))) - a)), -1.0);
}

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

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

def code(a, b):
	return math.exp(a) / (math.exp(a) + math.exp(b))
↓
def code(a, b):
	return math.pow(math.exp((math.log((math.exp(a) + math.exp(b))) - a)), -1.0)

function code(a, b)
	return Float64(exp(a) / Float64(exp(a) + exp(b)))
end
↓
function code(a, b)
	return exp(Float64(log(Float64(exp(a) + exp(b))) - a)) ^ -1.0
end

function tmp = code(a, b)
	tmp = exp(a) / (exp(a) + exp(b));
end
↓
function tmp = code(a, b)
	tmp = exp((log((exp(a) + exp(b))) - a)) ^ -1.0;
end

code[a_, b_] := N[(N[Exp[a], $MachinePrecision] / N[(N[Exp[a], $MachinePrecision] + N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[a_, b_] := N[Power[N[Exp[N[(N[Log[N[(N[Exp[a], $MachinePrecision] + N[Exp[b], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]], $MachinePrecision], -1.0], $MachinePrecision]

\frac{e^{a}}{e^{a} + e^{b}}
↓
{\left(e^{\log \left(e^{a} + e^{b}\right) - a}\right)}^{-1}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.0
Herbie0.5
\[\frac{1}{1 + e^{b - a}} \]

Derivation

  1. Initial program 0.6

    \[\frac{e^{a}}{e^{a} + e^{b}} \]

  2. Applied egg-rr0.6

    \[\leadsto \color{blue}{{\left(\frac{e^{a} + e^{b}}{e^{a}}\right)}^{-1}} \]

  3. Applied egg-rr0.5

    \[\leadsto {\color{blue}{\left(e^{\left(\log \left(e^{a} + e^{b}\right) - a\right) \cdot 1}\right)}}^{-1} \]

  4. Final simplification0.5

    \[\leadsto {\left(e^{\log \left(e^{a} + e^{b}\right) - a}\right)}^{-1} \]

Reproduce

herbie shell --seed 2022156 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

  (/ (exp a) (+ (exp a) (exp b))))