Average Error: 0.6 → 0.7
Time: 21.5s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\log \left(e^{\frac{e^{a}}{e^{a} + e^{b}}}\right)\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\log \left(e^{\frac{e^{a}}{e^{a} + e^{b}}}\right)
double f(double a, double b) {
        double r27655442 = a;
        double r27655443 = exp(r27655442);
        double r27655444 = b;
        double r27655445 = exp(r27655444);
        double r27655446 = r27655443 + r27655445;
        double r27655447 = r27655443 / r27655446;
        return r27655447;
}
↓
double f(double a, double b) {
        double r27655448 = a;
        double r27655449 = exp(r27655448);
        double r27655450 = b;
        double r27655451 = exp(r27655450);
        double r27655452 = r27655449 + r27655451;
        double r27655453 = r27655449 / r27655452;
        double r27655454 = exp(r27655453);
        double r27655455 = log(r27655454);
        return r27655455;
}

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-log-exp0.7

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

  4. Final simplification0.7

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

Reproduce

herbie shell --seed 2019125 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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