Average Error: 0.7 → 0.5
Time: 9.4s
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 r3517101 = a;
        double r3517102 = exp(r3517101);
        double r3517103 = b;
        double r3517104 = exp(r3517103);
        double r3517105 = r3517102 + r3517104;
        double r3517106 = r3517102 / r3517105;
        return r3517106;
}
↓
double f(double a, double b) {
        double r3517107 = a;
        double r3517108 = exp(r3517107);
        double r3517109 = b;
        double r3517110 = exp(r3517109);
        double r3517111 = r3517108 + r3517110;
        double r3517112 = log(r3517111);
        double r3517113 = r3517107 - r3517112;
        double r3517114 = exp(r3517113);
        return r3517114;
}

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
Herbie0.5
\[\frac{1}{1 + e^{b - a}}\]

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-exp0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2019135 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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