Average Error: 0.7 → 0.7
Time: 3.2s
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 r167599 = a;
        double r167600 = exp(r167599);
        double r167601 = b;
        double r167602 = exp(r167601);
        double r167603 = r167600 + r167602;
        double r167604 = r167600 / r167603;
        return r167604;
}
↓
double f(double a, double b) {
        double r167605 = a;
        double r167606 = exp(r167605);
        double r167607 = b;
        double r167608 = exp(r167607);
        double r167609 = r167606 + r167608;
        double r167610 = r167606 / r167609;
        return r167610;
}

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. Final simplification0.7

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

Reproduce

herbie shell --seed 2019322 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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