Average Error: 0.6 → 0.6
Time: 3.8s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[e^{\log \left(\frac{e^{a}}{e^{a} + e^{b}}\right)}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{\log \left(\frac{e^{a}}{e^{a} + e^{b}}\right)}
double f(double a, double b) {
        double r121551 = a;
        double r121552 = exp(r121551);
        double r121553 = b;
        double r121554 = exp(r121553);
        double r121555 = r121552 + r121554;
        double r121556 = r121552 / r121555;
        return r121556;
}
↓
double f(double a, double b) {
        double r121557 = a;
        double r121558 = exp(r121557);
        double r121559 = b;
        double r121560 = exp(r121559);
        double r121561 = r121558 + r121560;
        double r121562 = r121558 / r121561;
        double r121563 = log(r121562);
        double r121564 = exp(r121563);
        return r121564;
}

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 add-log-exp0.6

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

  7. Applied diff-log0.6

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

  8. Final simplification0.6

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

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))))