Average Error: 0.7 → 0.7
Time: 28.8s
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 r17579564 = a;
        double r17579565 = exp(r17579564);
        double r17579566 = b;
        double r17579567 = exp(r17579566);
        double r17579568 = r17579565 + r17579567;
        double r17579569 = r17579565 / r17579568;
        return r17579569;
}
↓
double f(double a, double b) {
        double r17579570 = a;
        double r17579571 = exp(r17579570);
        double r17579572 = b;
        double r17579573 = exp(r17579572);
        double r17579574 = r17579571 + r17579573;
        double r17579575 = r17579571 / r17579574;
        return r17579575;
}

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 2019112 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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