Average Error: 0.8 → 0.7
Time: 13.2s
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 r3977749 = a;
        double r3977750 = exp(r3977749);
        double r3977751 = b;
        double r3977752 = exp(r3977751);
        double r3977753 = r3977750 + r3977752;
        double r3977754 = r3977750 / r3977753;
        return r3977754;
}
↓
double f(double a, double b) {
        double r3977755 = a;
        double r3977756 = exp(r3977755);
        double r3977757 = b;
        double r3977758 = exp(r3977757);
        double r3977759 = r3977756 + r3977758;
        double r3977760 = log(r3977759);
        double r3977761 = r3977755 - r3977760;
        double r3977762 = exp(r3977761);
        return r3977762;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.8
Target0.0
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.8

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

  3. Applied add-exp-log0.8

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

  4. Applied div-exp0.7

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

  5. Final simplification0.7

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

Reproduce

herbie shell --seed 2019134 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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