Average Error: 0.7 → 0.7
Time: 12.6s
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 r4186541 = a;
        double r4186542 = exp(r4186541);
        double r4186543 = b;
        double r4186544 = exp(r4186543);
        double r4186545 = r4186542 + r4186544;
        double r4186546 = r4186542 / r4186545;
        return r4186546;
}
↓
double f(double a, double b) {
        double r4186547 = a;
        double r4186548 = exp(r4186547);
        double r4186549 = b;
        double r4186550 = exp(r4186549);
        double r4186551 = r4186548 + r4186550;
        double r4186552 = r4186548 / r4186551;
        return r4186552;
}

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
\[\frac{1.0}{1.0 + e^{b - a}}\]

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 2019165 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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