Average Error: 0.7 → 0.6
Time: 10.7s
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 r7655128 = a;
        double r7655129 = exp(r7655128);
        double r7655130 = b;
        double r7655131 = exp(r7655130);
        double r7655132 = r7655129 + r7655131;
        double r7655133 = r7655129 / r7655132;
        return r7655133;
}
↓
double f(double a, double b) {
        double r7655134 = a;
        double r7655135 = exp(r7655134);
        double r7655136 = b;
        double r7655137 = exp(r7655136);
        double r7655138 = r7655135 + r7655137;
        double r7655139 = log(r7655138);
        double r7655140 = r7655134 - r7655139;
        double r7655141 = exp(r7655140);
        return r7655141;
}

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. Final simplification0.6

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

Reproduce

herbie shell --seed 2019170 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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