Average Error: 0.7 → 0.7
Time: 14.4s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}
double f(double a, double b) {
        double r2947201 = a;
        double r2947202 = exp(r2947201);
        double r2947203 = b;
        double r2947204 = exp(r2947203);
        double r2947205 = r2947202 + r2947204;
        double r2947206 = r2947202 / r2947205;
        return r2947206;
}
↓
double f(double a, double b) {
        double r2947207 = 1.0;
        double r2947208 = a;
        double r2947209 = exp(r2947208);
        double r2947210 = b;
        double r2947211 = exp(r2947210);
        double r2947212 = r2947209 + r2947211;
        double r2947213 = r2947212 / r2947209;
        double r2947214 = r2947207 / r2947213;
        return r2947214;
}

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
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

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

  3. Applied clear-num0.7

    \[\leadsto \color{blue}{\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}}\]

  4. Final simplification0.7

    \[\leadsto \frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}\]

Reproduce

herbie shell --seed 2019171 +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))))