Average Error: 0.6 → 0.7
Time: 17.9s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\log \left({\left(e^{e^{a}}\right)}^{\left(\frac{1}{e^{a} + e^{b}}\right)}\right)\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\log \left({\left(e^{e^{a}}\right)}^{\left(\frac{1}{e^{a} + e^{b}}\right)}\right)
double f(double a, double b) {
        double r6816396 = a;
        double r6816397 = exp(r6816396);
        double r6816398 = b;
        double r6816399 = exp(r6816398);
        double r6816400 = r6816397 + r6816399;
        double r6816401 = r6816397 / r6816400;
        return r6816401;
}
↓
double f(double a, double b) {
        double r6816402 = a;
        double r6816403 = exp(r6816402);
        double r6816404 = exp(r6816403);
        double r6816405 = 1.0;
        double r6816406 = b;
        double r6816407 = exp(r6816406);
        double r6816408 = r6816403 + r6816407;
        double r6816409 = r6816405 / r6816408;
        double r6816410 = pow(r6816404, r6816409);
        double r6816411 = log(r6816410);
        return r6816411;
}

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

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 add-log-exp0.6

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

  7. Simplified0.7

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

  9. Applied div-inv0.7

    \[\leadsto \log \left(e^{\color{blue}{e^{a} \cdot \frac{1}{e^{a} + e^{b}}}}\right)\]

  10. Applied exp-prod0.7

    \[\leadsto \log \color{blue}{\left({\left(e^{e^{a}}\right)}^{\left(\frac{1}{e^{a} + e^{b}}\right)}\right)}\]

  11. Final simplification0.7

    \[\leadsto \log \left({\left(e^{e^{a}}\right)}^{\left(\frac{1}{e^{a} + e^{b}}\right)}\right)\]

Reproduce

herbie shell --seed 2019169 
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

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