Average Error: 0.7 → 0.8
Time: 11.5s
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 r116115 = a;
        double r116116 = exp(r116115);
        double r116117 = b;
        double r116118 = exp(r116117);
        double r116119 = r116116 + r116118;
        double r116120 = r116116 / r116119;
        return r116120;
}
↓
double f(double a, double b) {
        double r116121 = a;
        double r116122 = exp(r116121);
        double r116123 = b;
        double r116124 = exp(r116123);
        double r116125 = r116122 + r116124;
        double r116126 = r116122 / r116125;
        double r116127 = exp(r116126);
        double r116128 = log(r116127);
        return r116128;
}

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 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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