Average Error: 0.8 → 0.8
Time: 10.0s
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 r2786201 = a;
        double r2786202 = exp(r2786201);
        double r2786203 = b;
        double r2786204 = exp(r2786203);
        double r2786205 = r2786202 + r2786204;
        double r2786206 = r2786202 / r2786205;
        return r2786206;
}
↓
double f(double a, double b) {
        double r2786207 = a;
        double r2786208 = exp(r2786207);
        double r2786209 = b;
        double r2786210 = exp(r2786209);
        double r2786211 = r2786208 + r2786210;
        double r2786212 = r2786208 / r2786211;
        return r2786212;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.8
Target0.0
Herbie0.8
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.8

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

  2. Taylor expanded around inf 0.8

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

  3. Final simplification0.8

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

Reproduce

herbie shell --seed 2019152 +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))))