Average Error: 0.6 → 0.6
Time: 4.5s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[e^{a} \cdot \frac{1}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{a} \cdot \frac{1}{e^{a} + e^{b}}
double f(double a, double b) {
        double r163202 = a;
        double r163203 = exp(r163202);
        double r163204 = b;
        double r163205 = exp(r163204);
        double r163206 = r163203 + r163205;
        double r163207 = r163203 / r163206;
        return r163207;
}
↓
double f(double a, double b) {
        double r163208 = a;
        double r163209 = exp(r163208);
        double r163210 = 1.0;
        double r163211 = b;
        double r163212 = exp(r163211);
        double r163213 = r163209 + r163212;
        double r163214 = r163210 / r163213;
        double r163215 = r163209 * r163214;
        return r163215;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.0
Herbie0.6
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

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

  3. Applied div-inv0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2020047 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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