Average Error: 0.7 → 0.7
Time: 6.3s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{a} + e^{b}}
double f(double a, double b) {
        double r4981064 = a;
        double r4981065 = exp(r4981064);
        double r4981066 = b;
        double r4981067 = exp(r4981066);
        double r4981068 = r4981065 + r4981067;
        double r4981069 = r4981065 / r4981068;
        return r4981069;
}
↓
double f(double a, double b) {
        double r4981070 = a;
        double r4981071 = exp(r4981070);
        double r4981072 = b;
        double r4981073 = exp(r4981072);
        double r4981074 = r4981071 + r4981073;
        double r4981075 = r4981071 / r4981074;
        return r4981075;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.7
Target0.0
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

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

  2. Final simplification0.7

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

Reproduce

herbie shell --seed 2019165 
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1 (+ 1 (exp (- b a))))

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