Average Error: 0.7 → 0.8
Time: 20.9s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\log \left(e^{\frac{e^{a}}{e^{a} + e^{b}}}\right)\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\log \left(e^{\frac{e^{a}}{e^{a} + e^{b}}}\right)
double f(double a, double b) {
        double r6244680 = a;
        double r6244681 = exp(r6244680);
        double r6244682 = b;
        double r6244683 = exp(r6244682);
        double r6244684 = r6244681 + r6244683;
        double r6244685 = r6244681 / r6244684;
        return r6244685;
}
↓
double f(double a, double b) {
        double r6244686 = a;
        double r6244687 = exp(r6244686);
        double r6244688 = b;
        double r6244689 = exp(r6244688);
        double r6244690 = r6244687 + r6244689;
        double r6244691 = r6244687 / r6244690;
        double r6244692 = exp(r6244691);
        double r6244693 = log(r6244692);
        return r6244693;
}

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

Derivation

  1. Initial program 0.7

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

  3. Applied add-log-exp0.8

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

  4. Final simplification0.8

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

Reproduce

herbie shell --seed 2019162 +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))))