Average Error: 0.8 → 0.8
Time: 10.1s
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 r3201945 = a;
        double r3201946 = exp(r3201945);
        double r3201947 = b;
        double r3201948 = exp(r3201947);
        double r3201949 = r3201946 + r3201948;
        double r3201950 = r3201946 / r3201949;
        return r3201950;
}
↓
double f(double a, double b) {
        double r3201951 = a;
        double r3201952 = exp(r3201951);
        double r3201953 = b;
        double r3201954 = exp(r3201953);
        double r3201955 = r3201952 + r3201954;
        double r3201956 = r3201952 / r3201955;
        return r3201956;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.8
Target0.0
Herbie0.8
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.8

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

  2. Taylor expanded around inf 0.8

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

  3. Final simplification0.8

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

Reproduce

herbie shell --seed 2019152 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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