Average Error: 0.6 → 0.6
Time: 3.5s
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 r173315 = a;
        double r173316 = exp(r173315);
        double r173317 = b;
        double r173318 = exp(r173317);
        double r173319 = r173316 + r173318;
        double r173320 = r173316 / r173319;
        return r173320;
}
↓
double f(double a, double b) {
        double r173321 = a;
        double r173322 = exp(r173321);
        double r173323 = b;
        double r173324 = exp(r173323);
        double r173325 = r173322 + r173324;
        double r173326 = r173322 / r173325;
        return r173326;
}

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

Derivation

  1. Initial program 0.6

    \[\frac{e^{a}}{e^{a} + e^{b}}\]
  2. Using strategy rm

  3. Applied add-exp-log0.6

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

  4. Applied div-exp0.5

    \[\leadsto \color{blue}{e^{a - \log \left(e^{a} + e^{b}\right)}}\]
  5. Using strategy rm

  6. Applied exp-diff0.6

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

  7. Simplified0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2020056 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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