Average Error: 0.6 → 0.6
Time: 13.1s
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 r111561 = a;
        double r111562 = exp(r111561);
        double r111563 = b;
        double r111564 = exp(r111563);
        double r111565 = r111562 + r111564;
        double r111566 = r111562 / r111565;
        return r111566;
}
↓
double f(double a, double b) {
        double r111567 = a;
        double r111568 = exp(r111567);
        double r111569 = b;
        double r111570 = exp(r111569);
        double r111571 = r111568 + r111570;
        double r111572 = r111568 / r111571;
        return r111572;
}

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. Final simplification0.6

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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