Average Error: 0.7 → 0.7
Time: 2.4s
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 r132418 = a;
        double r132419 = exp(r132418);
        double r132420 = b;
        double r132421 = exp(r132420);
        double r132422 = r132419 + r132421;
        double r132423 = r132419 / r132422;
        return r132423;
}
↓
double f(double a, double b) {
        double r132424 = a;
        double r132425 = exp(r132424);
        double r132426 = b;
        double r132427 = exp(r132426);
        double r132428 = r132425 + r132427;
        double r132429 = r132425 / r132428;
        return r132429;
}

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. Using strategy rm

  3. Applied *-un-lft-identity0.7

    \[\leadsto \color{blue}{1 \cdot \frac{e^{a}}{e^{a} + e^{b}}}\]

  4. Final simplification0.7

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

Reproduce

herbie shell --seed 2020036 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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