Average Error: 0.7 → 0.7
Time: 41.8s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{a} + e^{b}}
double f(double a, double b) {
        double r17541158 = a;
        double r17541159 = exp(r17541158);
        double r17541160 = b;
        double r17541161 = exp(r17541160);
        double r17541162 = r17541159 + r17541161;
        double r17541163 = r17541159 / r17541162;
        return r17541163;
}
↓
double f(double a, double b) {
        double r17541164 = a;
        double r17541165 = exp(r17541164);
        double r17541166 = b;
        double r17541167 = exp(r17541166);
        double r17541168 = r17541165 + r17541167;
        double r17541169 = r17541165 / r17541168;
        return r17541169;
}

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. Taylor expanded around -inf 0.7

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

  3. Final simplification0.7

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

Reproduce

herbie shell --seed 2019128 
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1 (+ 1 (exp (- b a))))

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