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 r3898511 = a;
        double r3898512 = exp(r3898511);
        double r3898513 = b;
        double r3898514 = exp(r3898513);
        double r3898515 = r3898512 + r3898514;
        double r3898516 = r3898512 / r3898515;
        return r3898516;
}
↓
double f(double a, double b) {
        double r3898517 = a;
        double r3898518 = exp(r3898517);
        double r3898519 = b;
        double r3898520 = exp(r3898519);
        double r3898521 = r3898518 + r3898520;
        double r3898522 = log(r3898521);
        double r3898523 = r3898517 - r3898522;
        double r3898524 = exp(r3898523);
        return r3898524;
}

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 +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))))