Average Error: 0.7 → 0.6
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 r3677465 = a;
        double r3677466 = exp(r3677465);
        double r3677467 = b;
        double r3677468 = exp(r3677467);
        double r3677469 = r3677466 + r3677468;
        double r3677470 = r3677466 / r3677469;
        return r3677470;
}
↓
double f(double a, double b) {
        double r3677471 = a;
        double r3677472 = exp(r3677471);
        double r3677473 = b;
        double r3677474 = exp(r3677473);
        double r3677475 = r3677472 + r3677474;
        double r3677476 = log(r3677475);
        double r3677477 = r3677471 - r3677476;
        double r3677478 = exp(r3677477);
        return r3677478;
}

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 2019129 +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))))