Average Error: 0.7 → 0.7
Time: 6.8s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{b} + e^{a}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{b} + e^{a}}
double f(double a, double b) {
        double r62328 = a;
        double r62329 = exp(r62328);
        double r62330 = b;
        double r62331 = exp(r62330);
        double r62332 = r62329 + r62331;
        double r62333 = r62329 / r62332;
        return r62333;
}
↓
double f(double a, double b) {
        double r62334 = a;
        double r62335 = exp(r62334);
        double r62336 = b;
        double r62337 = exp(r62336);
        double r62338 = r62337 + r62335;
        double r62339 = r62335 / r62338;
        return r62339;
}

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. Taylor expanded around inf 0.7

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

  3. Final simplification0.7

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

Reproduce

herbie shell --seed 2019298 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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