Average Error: 0.7 → 0.8
Time: 11.6s
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 r148057 = a;
        double r148058 = exp(r148057);
        double r148059 = b;
        double r148060 = exp(r148059);
        double r148061 = r148058 + r148060;
        double r148062 = r148058 / r148061;
        return r148062;
}
↓
double f(double a, double b) {
        double r148063 = a;
        double r148064 = exp(r148063);
        double r148065 = b;
        double r148066 = exp(r148065);
        double r148067 = r148064 + r148066;
        double r148068 = r148064 / r148067;
        double r148069 = exp(r148068);
        double r148070 = log(r148069);
        return r148070;
}

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 2019199 
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

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