Average Error: 0.7 → 0.7
Time: 16.2s
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 r9100589 = a;
        double r9100590 = exp(r9100589);
        double r9100591 = b;
        double r9100592 = exp(r9100591);
        double r9100593 = r9100590 + r9100592;
        double r9100594 = r9100590 / r9100593;
        return r9100594;
}
↓
double f(double a, double b) {
        double r9100595 = a;
        double r9100596 = exp(r9100595);
        double r9100597 = b;
        double r9100598 = exp(r9100597);
        double r9100599 = r9100596 + r9100598;
        double r9100600 = r9100596 / r9100599;
        return r9100600;
}

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 2019174 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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