Average Error: 0.7 → 0.6
Time: 16.4s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[e^{a - \log \left(e^{b} + e^{a}\right)}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{a - \log \left(e^{b} + e^{a}\right)}
double f(double a, double b) {
        double r5885524 = a;
        double r5885525 = exp(r5885524);
        double r5885526 = b;
        double r5885527 = exp(r5885526);
        double r5885528 = r5885525 + r5885527;
        double r5885529 = r5885525 / r5885528;
        return r5885529;
}
↓
double f(double a, double b) {
        double r5885530 = a;
        double r5885531 = b;
        double r5885532 = exp(r5885531);
        double r5885533 = exp(r5885530);
        double r5885534 = r5885532 + r5885533;
        double r5885535 = log(r5885534);
        double r5885536 = r5885530 - r5885535;
        double r5885537 = exp(r5885536);
        return r5885537;
}

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

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

Reproduce

herbie shell --seed 2019200 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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