Average Error: 0.6 → 0.5
Time: 46.1s
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 r24777103 = a;
        double r24777104 = exp(r24777103);
        double r24777105 = b;
        double r24777106 = exp(r24777105);
        double r24777107 = r24777104 + r24777106;
        double r24777108 = r24777104 / r24777107;
        return r24777108;
}
↓
double f(double a, double b) {
        double r24777109 = a;
        double r24777110 = exp(r24777109);
        double r24777111 = b;
        double r24777112 = exp(r24777111);
        double r24777113 = r24777110 + r24777112;
        double r24777114 = log(r24777113);
        double r24777115 = r24777109 - r24777114;
        double r24777116 = exp(r24777115);
        return r24777116;
}

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

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. Final simplification0.5

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

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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