Average Error: 0.7 → 0.6
Time: 9.6s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[e^{a - \log \left(e^{a} + e^{b}\right)}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{a - \log \left(e^{a} + e^{b}\right)}
double f(double a, double b) {
        double r78319 = a;
        double r78320 = exp(r78319);
        double r78321 = b;
        double r78322 = exp(r78321);
        double r78323 = r78320 + r78322;
        double r78324 = r78320 / r78323;
        return r78324;
}
↓
double f(double a, double b) {
        double r78325 = a;
        double r78326 = exp(r78325);
        double r78327 = b;
        double r78328 = exp(r78327);
        double r78329 = r78326 + r78328;
        double r78330 = log(r78329);
        double r78331 = r78325 - r78330;
        double r78332 = exp(r78331);
        return r78332;
}

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

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. Simplified0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2019196 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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