Average Error: 0.7 → 0.7
Time: 3.2s
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 r118538 = a;
        double r118539 = exp(r118538);
        double r118540 = b;
        double r118541 = exp(r118540);
        double r118542 = r118539 + r118541;
        double r118543 = r118539 / r118542;
        return r118543;
}
↓
double f(double a, double b) {
        double r118544 = a;
        double r118545 = exp(r118544);
        double r118546 = b;
        double r118547 = exp(r118546);
        double r118548 = r118545 + r118547;
        double r118549 = r118545 / r118548;
        double r118550 = log(r118549);
        double r118551 = exp(r118550);
        return r118551;
}

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 add-exp-log0.7

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

  4. Applied div-exp0.6

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

  6. Applied add-log-exp0.7

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

  7. Applied diff-log0.7

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

  8. Final simplification0.7

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

Reproduce

herbie shell --seed 2020020 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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