Average Error: 0.7 → 0.7
Time: 16.7s
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 r3477807 = a;
        double r3477808 = exp(r3477807);
        double r3477809 = b;
        double r3477810 = exp(r3477809);
        double r3477811 = r3477808 + r3477810;
        double r3477812 = r3477808 / r3477811;
        return r3477812;
}
↓
double f(double a, double b) {
        double r3477813 = a;
        double r3477814 = exp(r3477813);
        double r3477815 = b;
        double r3477816 = exp(r3477815);
        double r3477817 = r3477814 + r3477816;
        double r3477818 = r3477814 / r3477817;
        return r3477818;
}

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 2019163 +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))))