Average Error: 0.5 → 0.4
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 r4832544 = a;
        double r4832545 = exp(r4832544);
        double r4832546 = b;
        double r4832547 = exp(r4832546);
        double r4832548 = r4832545 + r4832547;
        double r4832549 = r4832545 / r4832548;
        return r4832549;
}
↓
double f(double a, double b) {
        double r4832550 = a;
        double r4832551 = exp(r4832550);
        double r4832552 = b;
        double r4832553 = exp(r4832552);
        double r4832554 = r4832551 + r4832553;
        double r4832555 = log(r4832554);
        double r4832556 = r4832550 - r4832555;
        double r4832557 = exp(r4832556);
        return r4832557;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.5
Target0.0
Herbie0.4
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.5

    \[\frac{e^{a}}{e^{a} + e^{b}}\]
  2. Using strategy rm

  3. Applied add-exp-log0.5

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

  4. Applied div-exp0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019138 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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